diff --git a/index.html b/index.html
index 58bec0d..66fd189 100644
--- a/index.html
+++ b/index.html
@@ -22,7 +22,7 @@
<meta></meta>
</head>
<body><div id="root"></div>
- <script>window.logseq_db="[logseq____"~#datascript/DBlogseq____",[logseq____"^ logseq____",logseq____"~:schemalogseq____",[logseq____"^ logseq____",logseq____"~:ast/versionlogseq____",[logseq____"^ logseq____"],logseq____"~:file/contentlogseq____",[logseq____"^ logseq____"],logseq____"~:block/properties-text-valueslogseq____",[logseq____"^ logseq____"],logseq____"~:block/aliaslogseq____",[logseq____"^ logseq____",logseq____"~:db/valueTypelogseq____",logseq____"~:db.type/reflogseq____",logseq____"~:db/cardinalitylogseq____",logseq____"~:db.cardinality/manylogseq____"],logseq____"~:block/pre-block?logseq____",[logseq____"^ logseq____"],logseq____"~:block/uuidlogseq____",[logseq____"^ logseq____",logseq____"~:db/uniquelogseq____",logseq____"~:db.unique/identitylogseq____"],logseq____"~:block/prioritylogseq____",[logseq____"^ logseq____"],logseq____"~:block/propertieslogseq____",[logseq____"^ logseq____"],logseq____"~:block/journal?logseq____",[logseq____"^ logseq____"],logseq____"~:block/namespacelogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____"],logseq____"~:block/updated-atlogseq____",[logseq____"^ logseq____"],logseq____"~:block/repeated?logseq____",[logseq____"^ logseq____"],logseq____"~:db/typelogseq____",[logseq____"^ logseq____"],logseq____"~:file/handlelogseq____",[logseq____"^ logseq____"],logseq____"~:block/leftlogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"~:db/indexlogseq____",true],logseq____"~:block/refslogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^8logseq____",logseq____"^9logseq____"],logseq____"~:block/scheduledlogseq____",[logseq____"^ logseq____"],logseq____"~:block/properties-orderlogseq____",[logseq____"^ logseq____"],logseq____"~:block/created-atlogseq____",[logseq____"^ logseq____"],logseq____"~:block/deadlinelogseq____",[logseq____"^ logseq____"],logseq____"~:block/collapsed?logseq____",[logseq____"^ logseq____",logseq____"^Glogseq____",true],logseq____"~:block/journal-daylogseq____",[logseq____"^ logseq____"],logseq____"~:block/formatlogseq____",[logseq____"^ logseq____"],logseq____"~:block/tagslogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^8logseq____",logseq____"^9logseq____"],logseq____"~:block/contentlogseq____",[logseq____"^ logseq____"],logseq____"~:recent/pageslogseq____",[logseq____"^ logseq____"],logseq____"~:block/macroslogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^8logseq____",logseq____"^9logseq____"],logseq____"~:db/identlogseq____",[logseq____"^ logseq____",logseq____"^logseq____<logseq____",logseq____"^=logseq____"],logseq____"~:block/path-refslogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^8logseq____",logseq____"^9logseq____"],logseq____"~:block/parentlogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^Glogseq____",true],logseq____"~:block/typelogseq____",[logseq____"^ logseq____"],logseq____"~:block/pagelogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^Glogseq____",true],logseq____"~:block/namelogseq____",[logseq____"^ logseq____",logseq____"^logseq____<logseq____",logseq____"^=logseq____"],logseq____"~:file/pathlogseq____",[logseq____"^ logseq____",logseq____"^logseq____<logseq____",logseq____"^=logseq____"],logseq____"~:block/filelogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____"],logseq____"~:block/markerlogseq____",[logseq____"^ logseq____"],logseq____"~:block/original-namelogseq____",[logseq____"^ logseq____",logseq____"^logseq____<logseq____",logseq____"^=logseq____"],logseq____"~:schema/versionlogseq____",[logseq____"^ logseq____"]],logseq____"~:datomslogseq____",[logseq____"~#listlogseq____",[[logseq____"~#datascript/Datomlogseq____",[1,logseq____"^12logseq____",2,536870913]],[logseq____"^15logseq____",[2,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[2,logseq____"^Ylogseq____",logseq____"cardlogseq____",536870913]],[logseq____"^15logseq____",[2,logseq____"^11logseq____",logseq____"cardlogseq____",536870913]],[logseq____"^15logseq____",[2,logseq____"^;logseq____",logseq____"~uc8211c75-55cc-44dd-9ce1-9062c0005cb5logseq____",536870914]],[logseq____"^15logseq____",[3,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[3,logseq____"^Ylogseq____",logseq____"canceledlogseq____",536870914]],[logseq____"^15logseq____",[3,logseq____"^11logseq____",logseq____"CANCELEDlogseq____",536870914]],[logseq____"^15logseq____",[3,logseq____"^;logseq____",logseq____"~u3672ada5-9526-487a-bf97-78a6ae419bf9logseq____",536870914]],[logseq____"^15logseq____",[4,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[4,logseq____"^Ylogseq____",logseq____"todologseq____",536870914]],[logseq____"^15logseq____",[4,logseq____"^11logseq____",logseq____"TODOlogseq____",536870914]],[logseq____"^15logseq____",[4,logseq____"^;logseq____",logseq____"~u10e66557-dfbb-4f3f-a220-1e26e1baa499logseq____",536870914]],[logseq____"^15logseq____",[5,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[5,logseq____"^Ylogseq____",logseq____"nowlogseq____",536870914]],[logseq____"^15logseq____",[5,logseq____"^11logseq____",logseq____"NOWlogseq____",536870914]],[logseq____"^15logseq____",[5,logseq____"^;logseq____",logseq____"~u5dfce600-450c-4b5c-a8fd-eaa343e83921logseq____",536870914]],[logseq____"^15logseq____",[6,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[6,logseq____"^Ylogseq____",logseq____"laterlogseq____",536870914]],[logseq____"^15logseq____",[6,logseq____"^11logseq____",logseq____"LATERlogseq____",536870914]],[logseq____"^15logseq____",[6,logseq____"^;logseq____",logseq____"~u23f06527-1e02-47e0-b5cb-96c1b7dc3ed6logseq____",536870914]],[logseq____"^15logseq____",[7,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[7,logseq____"^Ylogseq____",logseq____"donelogseq____",536870914]],[logseq____"^15logseq____",[7,logseq____"^11logseq____",logseq____"DONElogseq____",536870914]],[logseq____"^15logseq____",[7,logseq____"^;logseq____",logseq____"~uc35f34b2-3fb0-4dbc-99ef-7b6b0c0f21e6logseq____",536870914]],[logseq____"^15logseq____",[8,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[8,logseq____"^Ylogseq____",logseq____"doinglogseq____",536870914]],[logseq____"^15logseq____",[8,logseq____"^11logseq____",logseq____"DOINGlogseq____",536870914]],[logseq____"^15logseq____",[8,logseq____"^;logseq____",logseq____"~uf99f1f92-33e3-4717-bdd7-93e4733a7de4logseq____",536870914]],[logseq____"^15logseq____",[9,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[9,logseq____"^Ylogseq____",logseq____"in-progresslogseq____",536870914]],[logseq____"^15logseq____",[9,logseq____"^11logseq____",logseq____"IN-PROGRESSlogseq____",536870914]],[logseq____"^15logseq____",[9,logseq____"^;logseq____",logseq____"~ud8fb9831-72c4-4f84-bc99-f16dd44e4fa5logseq____",536870914]],[logseq____"^15logseq____",[10,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[10,logseq____"^Ylogseq____",logseq____"clogseq____",536870914]],[logseq____"^15logseq____",[10,logseq____"^11logseq____",logseq____"Clogseq____",536870914]],[logseq____"^15logseq____",[10,logseq____"^;logseq____",logseq____"~u9be4cffa-91f0-414e-a927-e85f4808041elogseq____",536870914]],[logseq____"^15logseq____",[11,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[11,logseq____"^Ylogseq____",logseq____"blogseq____",536870914]],[logseq____"^15logseq____",[11,logseq____"^11logseq____",logseq____"Blogseq____",536870914]],[logseq____"^15logseq____",[11,logseq____"^;logseq____",logseq____"~udec62a5b-3da3-4d12-97d8-e642e7a1cc13logseq____",536870914]],[logseq____"^15logseq____",[12,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[12,logseq____"^Ylogseq____",logseq____"contentslogseq____",536870914]],[logseq____"^15logseq____",[12,logseq____"^11logseq____",logseq____"contentslogseq____",536870917]],[logseq____"^15logseq____",[12,logseq____"^;logseq____",logseq____"~u6531e477-a417-45f2-9663-902d626944ealogseq____",536870917]],[logseq____"^15logseq____",[13,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[13,logseq____"^Ylogseq____",logseq____"waitinglogseq____",536870914]],[logseq____"^15logseq____",[13,logseq____"^11logseq____",logseq____"WAITINGlogseq____",536870914]],[logseq____"^15logseq____",[13,logseq____"^;logseq____",logseq____"~u11d675d2-cc90-4bae-b366-90e4a78856e1logseq____",536870914]],[logseq____"^15logseq____",[14,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[14,logseq____"^Ylogseq____",logseq____"favoriteslogseq____",536870914]],[logseq____"^15logseq____",[14,logseq____"^11logseq____",logseq____"Favoriteslogseq____",536870914]],[logseq____"^15logseq____",[14,logseq____"^;logseq____",logseq____"~u7f0ec3f2-ca4a-4803-9ddc-ec67f237a1delogseq____",536870914]],[logseq____"^15logseq____",[15,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[15,logseq____"^Ylogseq____",logseq____"alogseq____",536870914]],[logseq____"^15logseq____",[15,logseq____"^11logseq____",logseq____"Alogseq____",536870914]],[logseq____"^15logseq____",[15,logseq____"^;logseq____",logseq____"~ubda82b9e-886b-4dca-82a0-ca76f368de5flogseq____",536870914]],[logseq____"^15logseq____",[16,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[16,logseq____"^Ylogseq____",logseq____"cancelledlogseq____",536870914]],[logseq____"^15logseq____",[16,logseq____"^11logseq____",logseq____"CANCELLEDlogseq____",536870914]],[logseq____"^15logseq____",[16,logseq____"^;logseq____",logseq____"~ua9faa653-963b-4a48-86da-d69aad15e294logseq____",536870914]],[logseq____"^15logseq____",[17,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[17,logseq____"^Ylogseq____",logseq____"waitlogseq____",536870914]],[logseq____"^15logseq____",[17,logseq____"^11logseq____",logseq____"WAITlogseq____",536870914]],[logseq____"^15logseq____",[17,logseq____"^;logseq____",logseq____"~u04e93664-97e8-4e48-8c0d-e183c6d5f743logseq____",536870914]],[logseq____"^15logseq____",[21,logseq____"^Qlogseq____",logseq____"logseq____",536870917]],[logseq____"^15logseq____",[21,logseq____"^Ologseq____",logseq____"~:markdownlogseq____",536870917]],[logseq____"^15logseq____",[21,logseq____"^Flogseq____",12,536870917]],[logseq____"^15logseq____",[21,logseq____"^Xlogseq____",12,536870917]],[logseq____"^15logseq____",[21,logseq____"^Vlogseq____",12,536870917]],[logseq____"^15logseq____",[21,logseq____"^Ulogseq____",12,536870917]],[logseq____"^15logseq____",[21,logseq____"~:block/unorderedlogseq____",true,536870917]],[logseq____"^15logseq____",[21,logseq____"^;logseq____",logseq____"~u6531e477-0691-47a7-b8f2-99a8faf60938logseq____",536870917]],[logseq____"^15logseq____",[23,logseq____"^Klogseq____",1697393389662,536870918]],[logseq____"^15logseq____",[23,logseq____"^Ylogseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",536870918]],[logseq____"^15logseq____",[23,logseq____"^11logseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",536870918]],[logseq____"^15logseq____",[23,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:ls-typelogseq____",logseq____"~:whiteboard-pagelogseq____",logseq____"~:logseq.tldraw.pagelogseq____",[logseq____"^ logseq____",logseq____"~:idlogseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"~:namelogseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"~:bindingslogseq____",[logseq____"^ logseq____"],logseq____"~:noncelogseq____",1,logseq____"~:assetslogseq____",[],logseq____"~:shapes-indexlogseq____",[logseq____"^14logseq____",[logseq____"1218f800-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"124a8f50-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"12857570-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"131c3730-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"13534cc0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"138706f0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"144e0070-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"147dea10-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"15145db0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"1bf58910-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"1c996a30-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"1e1beb80-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"1f082040-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"208b16c0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"5f510900-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"60d8ba70-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"617807b0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"61f80d20-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"627182e0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"62cf5a50-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"63cfda60-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"6458e080-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"65cf2cd0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"729dadb0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"73582410-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"7c681650-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"7d355160-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"80b57770-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"86fad800-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"d0839ca0-6b86-11ee-a673-27a2873cc90flogseq____"]]]],536870918]],[logseq____"^15logseq____",[23,logseq____"^Wlogseq____",logseq____"whiteboardlogseq____",536870918]],[logseq____"^15logseq____",[23,logseq____"^Blogseq____",1697393726609,536870918]],[logseq____"^15logseq____",[23,logseq____"^;logseq____",logseq____"~u652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",536870918]],[logseq____"^15logseq____",[24,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[24,logseq____"^Klogseq____",1697393537081,536870918]],[logseq____"^15logseq____",[24,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[24,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[24,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[24,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"~:whiteboard-shapelogseq____",logseq____"~:logseq.tldraw.shapelogseq____",[logseq____"^ logseq____",logseq____"~:strokelogseq____",logseq____"logseq____",logseq____"~:indexlogseq____",13,logseq____"~:scalelogseq____",[1,1],logseq____"~:scaleLevellogseq____",logseq____"mdlogseq____",logseq____"~:filllogseq____",logseq____"logseq____",logseq____"~:typelogseq____",logseq____"pencillogseq____",logseq____"~:pointslogseq____",[[0,0,0]],logseq____"~:strokeTypelogseq____",logseq____"linelogseq____",logseq____"~:strokeWidthlogseq____",2,logseq____"~:opacitylogseq____",1,logseq____"^1;logseq____",logseq____"208b16c0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"~:noFilllogseq____",true,logseq____"~:pointlogseq____",[2729.5,540.5],logseq____"~:parentIdlogseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393431086,logseq____"~:isCompletelogseq____",true]],536870918]],[logseq____"^15logseq____",[24,logseq____"^Blogseq____",1697393537081,536870918]],[logseq____"^15logseq____",[24,logseq____"^;logseq____",logseq____"~u208b16c0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[25,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[25,logseq____"^Klogseq____",1697393407539,536870918]],[logseq____"^15logseq____",[25,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[25,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[25,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[25,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",0,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,12,0],[1,25,0],[1,29,0],[1,51,0],[2,55,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"1218f800-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[371.5,205.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393406855,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[25,logseq____"^Blogseq____",1697393407539,536870918]],[logseq____"^15logseq____",[25,logseq____"^;logseq____",logseq____"~u1218f800-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[26,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[26,logseq____"^Klogseq____",1697393603730,536870918]],[logseq____"^15logseq____",[26,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[26,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[26,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[26,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",27,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[1,1,0],[9,5,0],[39,15,0],[79,22,0],[103,26,0],[153,35,0],[179,39,0],[244,42,0],[281,39,0],[353,31,0],[384,28,0],[432,25,0],[451,26,0],[481,27,0],[486,27,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"80b57770-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1130.5,980.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393592440,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[26,logseq____"^Blogseq____",1697393603730,536870918]],[logseq____"^15logseq____",[26,logseq____"^;logseq____",logseq____"~u80b57770-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[27,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[27,logseq____"^Klogseq____",1697393542656,536870918]],[logseq____"^15logseq____",[27,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[27,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[27,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[27,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",18,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[1,1,0],[2,4,0],[6,9,0],[12,27,0],[15,37,0],[22,54,0],[27,70,0],[33,86,0],[38,99,0],[43,112,0],[52,126,0],[54,129,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"627182e0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[543.5,422.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393541660,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[27,logseq____"^Blogseq____",1697393542656,536870918]],[logseq____"^15logseq____",[27,logseq____"^;logseq____",logseq____"~u627182e0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[28,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[28,logseq____"^Klogseq____",1697393726609,536870918]],[logseq____"^15logseq____",[28,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[28,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[28,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[28,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",28,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,1,0],[1,3,0],[3,8,0],[10,21,0],[16,43,0],[21,55,0],[34,81,0],[42,94,0],[60,121,0],[70,133,0],[87,150,0],[106,167,0],[132,188,0],[147,199,0],[174,218,0],[188,227,0],[216,246,0],[230,254,0],[262,272,0],[279,281,0],[296,289,0],[331,302,0],[349,309,0],[388,320,0],[407,324,0],[445,333,0],[461,337,0],[490,346,0],[502,350,0],[521,359,0],[531,364,0],[537,367,0],[540,368,0],[541,368,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"86fad800-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1102.5,513.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393602981,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[28,logseq____"^Blogseq____",1697393726609,536870918]],[logseq____"^15logseq____",[28,logseq____"^;logseq____",logseq____"~u86fad800-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[29,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[29,logseq____"^Klogseq____",1697393545356,536870918]],[logseq____"^15logseq____",[29,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[29,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[29,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[29,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",20,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[80,0,0],[79,1,0],[78,3,0],[74,11,0],[69,19,0],[67,24,0],[64,29,0],[63,32,0],[58,40,0],[54,45,0],[45,60,0],[42,67,0],[36,78,0],[33,84,0],[28,93,0],[26,97,0],[23,102,0],[21,105,0],[17,111,0],[14,115,0],[8,127,0],[0,144,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"63cfda60-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[780.5,415.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393543965,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[29,logseq____"^Blogseq____",1697393545356,536870918]],[logseq____"^15logseq____",[29,logseq____"^;logseq____",logseq____"~u63cfda60-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[30,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[30,logseq____"^Klogseq____",1697393587383,536870918]],[logseq____"^15logseq____",[30,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[30,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[30,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[30,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",25,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,1,0],[1,5,0],[3,11,0],[5,22,0],[7,28,0],[8,31,0],[10,34,0],[11,36,0],[14,38,0],[16,39,0],[17,39,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"7c681650-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1021.5,876.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393585218,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[30,logseq____"^Blogseq____",1697393587383,536870918]],[logseq____"^15logseq____",[30,logseq____"^;logseq____",logseq____"~u7c681650-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[31,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[31,logseq____"^Klogseq____",1697393592918,536870918]],[logseq____"^15logseq____",[31,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[31,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[31,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[31,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",26,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,1,0],[0,3,0],[0,6,0],[0,10,0],[2,19,0],[4,23,0],[4,25,0],[6,33,0],[7,36,0],[8,42,0],[9,46,0],[10,53,0],[10,56,0],[10,62,0],[10,64,0],[10,69,0],[10,72,0],[10,77,0],[10,79,0],[10,84,0],[10,85,0],[10,89,0],[10,90,0],[10,94,0],[10,95,0],[10,97,0],[10,98,0],[10,99,0],[9,100,0],[8,101,0],[8,102,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"7d355160-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1032.5,856.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393586583,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[31,logseq____"^Blogseq____",1697393592918,536870918]],[logseq____"^15logseq____",[31,logseq____"^;logseq____",logseq____"~u7d355160-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[32,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[32,logseq____"^Klogseq____",1697393412412,536870918]],[logseq____"^15logseq____",[32,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[32,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[32,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[32,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",6,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,2,0],[0,7,0],[1,17,0],[1,22,0],[1,38,0],[1,49,0],[0,64,0],[0,70,0],[2,76,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"144e0070-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1680.5,145.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393410562,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[32,logseq____"^Blogseq____",1697393412412,536870918]],[logseq____"^15logseq____",[32,logseq____"^;logseq____",logseq____"~u144e0070-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Klogseq____",1697393585666,536870918]],[logseq____"^15logseq____",[33,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[33,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[33,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",24,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[1,0,0],[1,1,0],[1,6,0],[3,21,0],[3,27,0],[4,40,0],[5,63,0],[5,87,0],[4,101,0],[2,128,0],[1,140,0],[0,167,0],[2,186,0],[3,206,0],[4,218,0],[6,248,0],[8,265,0],[13,301,0],[15,316,0],[20,348,0],[21,361,0],[23,384,0],[23,395,0],[25,407,0],[26,414,0],[28,423,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"73582410-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[952.5,462.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393570028,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[33,logseq____"^Blogseq____",1697393585666,536870918]],[logseq____"^15logseq____",[33,logseq____"^;logseq____",logseq____"~u73582410-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Klogseq____",1697393425130,536870918]],[logseq____"^15logseq____",[34,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[34,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[34,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",9,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,1,0],[0,4,0],[0,10,0],[0,31,0],[1,45,0],[3,66,0],[5,86,0],[7,102,0],[9,117,0],[8,134,0],[7,138,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"1bf58910-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1604.5,577.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393423406,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[34,logseq____"^Blogseq____",1697393425130,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u1bf58910-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Klogseq____",1697393541207,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[35,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[35,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",16,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[76,0,0],[75,0,0],[75,1,0],[74,5,0],[71,9,0],[66,18,0],[63,24,0],[53,39,0],[49,43,0],[43,52,0],[41,56,0],[35,62,0],[32,67,0],[21,82,0],[14,91,0],[0,104,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"617807b0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[369.5,430.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393540028,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[35,logseq____"^Blogseq____",1697393541207,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u617807b0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Klogseq____",1697393570618,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[36,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[36,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",23,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[1,1,0],[2,3,0],[4,6,0],[12,14,0],[24,25,0],[38,37,0],[56,48,0],[67,53,0],[87,59,0],[106,65,0],[120,68,0],[147,71,0],[167,70,0],[184,66,0],[195,62,0],[197,62,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"729dadb0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[784.5,867.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393568797,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[36,logseq____"^Blogseq____",1697393570618,536870918]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u729dadb0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[37,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[37,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",29,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[3,4,0],[0,1,0],[0,0,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"d0839ca0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[2035.5,540.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393726318,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[37,logseq____"^Blogseq____",1697393726610,536870918]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~ud0839ca0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Klogseq____",1697393539383,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[38,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[38,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",14,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[124,0,0],[119,4,0],[118,5,0],[117,6,0],[115,8,0],[111,13,0],[110,15,0],[109,17,0],[106,19,0],[101,23,0],[95,28,0],[92,32,0],[88,36,0],[79,46,0],[71,54,0],[61,62,0],[56,67,0],[46,78,0],[42,84,0],[31,94,0],[21,104,0],[10,117,0],[2,126,0],[0,129,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"5f510900-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[238.5,402.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393536425,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[38,logseq____"^Blogseq____",1697393539383,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u5f510900-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Klogseq____",1697393412413,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[39,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[39,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",7,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[14,0,0],[13,2,0],[13,8,0],[8,31,0],[5,45,0],[0,95,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"147dea10-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1777.5,148.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393410872,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[39,logseq____"^Blogseq____",1697393412413,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u147dea10-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Klogseq____",1697393429358,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[40,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",11,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,178,0],[0,179,0],[4,181,0],[124,202,0],[143,201,0],[186,195,0],[223,185,0],[261,169,0],[286,157,0],[332,135,0],[352,123,0],[385,101,0],[399,90,0],[423,66,0],[435,53,0],[458,32,0],[467,24,0],[480,12,0],[496,0,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"1e1beb80-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1838.5,676.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393427020,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[40,logseq____"^Blogseq____",1697393429358,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u1e1beb80-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Klogseq____",1697393544592,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[41,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[41,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",19,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,1,0],[0,6,0],[0,14,0],[1,31,0],[2,40,0],[3,52,0],[4,58,0],[7,67,0],[8,71,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"62cf5a50-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[625.5,628.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393542273,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[41,logseq____"^Blogseq____",1697393544592,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u62cf5a50-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Klogseq____",1697393409577,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[42,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[42,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",4,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[16,0,0],[16,1,0],[13,16,0],[9,34,0],[1,70,0],[0,79,0],[0,87,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"13534cc0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[962.5,190.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393408916,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[42,logseq____"^Blogseq____",1697393409577,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u13534cc0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Klogseq____",1697393411189,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[43,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[43,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",5,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[6,0,0],[6,1,0],[5,2,0],[4,12,0],[2,30,0],[0,44,0],[0,70,0],[2,96,0],[4,111,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"138706f0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1067.5,173.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393409257,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[43,logseq____"^Blogseq____",1697393411189,536870918]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u138706f0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Klogseq____",1697393431361,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[44,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",12,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[2,4,0],[5,14,0],[12,47,0],[14,65,0],[19,91,0],[21,103,0],[27,125,0],[32,137,0],[46,161,0],[68,188,0],[80,200,0],[92,212,0],[117,234,0],[130,243,0],[159,263,0],[173,270,0],[203,279,0],[219,282,0],[251,282,0],[267,282,0],[300,274,0],[319,269,0],[354,253,0],[371,245,0],[406,223,0],[422,212,0],[444,194,0],[465,178,0],[490,156,0],[501,147,0],[515,134,0],[526,126,0],[534,122,0],[538,121,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"1f082040-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1801.5,308.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393428584,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[44,logseq____"^Blogseq____",1697393431361,536870918]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u1f082040-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Klogseq____",1697393540523,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[45,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",15,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,2,0],[0,4,0],[1,12,0],[3,39,0],[3,56,0],[4,71,0],[5,84,0],[6,96,0],[6,102,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"60d8ba70-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[189.5,681.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393538978,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[45,logseq____"^Blogseq____",1697393540523,536870918]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u60d8ba70-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Klogseq____",1697393407903,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[46,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",1,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,3,0],[0,8,0],[0,24,0],[0,34,0],[1,48,0],[1,52,0],[2,67,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"124a8f50-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[436.5,217.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393407182,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[46,logseq____"^Blogseq____",1697393407903,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u124a8f50-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Klogseq____",1697393409239,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[47,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",3,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[20,0,0],[20,1,0],[19,5,0],[15,19,0],[11,32,0],[4,55,0],[1,65,0],[0,75,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"131c3730-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[869.5,181.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393408556,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[47,logseq____"^Blogseq____",1697393409239,536870918]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u131c3730-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Klogseq____",1697393542082,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[48,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",17,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[0,2,0],[2,14,0],[3,29,0],[4,48,0],[5,67,0],[5,84,0],[7,129,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"61f80d20-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[341.5,646.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393540859,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[48,logseq____"^Blogseq____",1697393542082,536870918]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u61f80d20-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Klogseq____",1697393423797,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[49,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",8,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,0,0],[1,4,0],[5,8,0],[15,18,0],[22,23,0],[38,34,0],[48,38,0],[60,43,0],[79,48,0],[106,49,0],[122,50,0],[136,50,0],[164,47,0],[178,45,0],[207,41,0],[238,35,0],[252,32,0],[274,29,0],[296,24,0],[310,20,0],[316,18,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"15145db0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[558.5,351.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393411873,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[49,logseq____"^Blogseq____",1697393423797,536870918]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u15145db0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Klogseq____",1697393427775,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[50,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",10,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[1,0,0],[1,2,0],[0,9,0],[0,18,0],[0,29,0],[1,39,0],[2,55,0],[4,65,0],[7,78,0],[10,87,0],[23,106,0],[30,113,0],[51,131,0],[63,139,0],[90,152,0],[102,156,0],[131,165,0],[143,168,0],[174,174,0],[191,176,0],[215,177,0],[237,177,0],[261,176,0],[269,175,0],[284,176,0],[291,176,0],[295,175,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"1c996a30-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[1203.5,403.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393424495,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[50,logseq____"^Blogseq____",1697393427775,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u1c996a30-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Klogseq____",1697393547842,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[51,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",21,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[11,0,0],[11,1,0],[11,2,0],[11,9,0],[10,13,0],[9,21,0],[9,24,0],[9,32,0],[8,35,0],[7,42,0],[5,49,0],[3,62,0],[1,67,0],[0,76,0],[0,78,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"6458e080-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[755.5,644.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393544856,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[51,logseq____"^Blogseq____",1697393547842,536870918]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u6458e080-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Klogseq____",1697393408892,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[52,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",2,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[3,0,0],[3,1,0],[3,3,0],[2,11,0],[1,35,0],[0,49,0],[0,59,0],[0,63,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"12857570-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[548.5,206.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393407568,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[52,logseq____"^Blogseq____",1697393408892,536870918]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u12857570-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"whiteboard pencillogseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Klogseq____",1697393569296,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",23,536870918]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",23,536870918]],[logseq____"^15logseq____",[53,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",logseq____"^1Alogseq____",logseq____"^1Blogseq____",[logseq____"^ logseq____",logseq____"^1Clogseq____",logseq____"logseq____",logseq____"^1Dlogseq____",22,logseq____"^1Elogseq____",[1,1],logseq____"^1Flogseq____",logseq____"mdlogseq____",logseq____"^1Glogseq____",logseq____"logseq____",logseq____"^1Hlogseq____",logseq____"pencillogseq____",logseq____"^1Ilogseq____",[[0,70,0],[1,71,0],[7,72,0],[30,77,0],[36,77,0],[46,77,0],[56,77,0],[80,73,0],[93,69,0],[115,61,0],[135,52,0],[159,43,0],[180,34,0],[202,23,0],[219,14,0],[228,9,0],[243,2,0],[248,1,0],[249,0,0]],logseq____"^1Jlogseq____",logseq____"linelogseq____",logseq____"^1Klogseq____",2,logseq____"^1Llogseq____",1,logseq____"^1;logseq____",logseq____"65cf2cd0-6b86-11ee-a673-27a2873cc90flogseq____",logseq____"^1Mlogseq____",true,logseq____"^1Nlogseq____",[355.5,850.5],logseq____"^1Ologseq____",logseq____"652c2aed-da8b-4770-9a77-c4ea035fa51dlogseq____",logseq____"^1logseq____>logseq____",1697393547313,logseq____"^1Plogseq____",true]],536870918]],[logseq____"^15logseq____",[53,logseq____"^Blogseq____",1697393569296,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u65cf2cd0-6b86-11ee-a673-27a2873cc90flogseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Klogseq____",1697768567626,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[56,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ylogseq____",logseq____"auffrischung mathematiklogseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^11logseq____",logseq____"Auffrischung Mathematiklogseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Blogseq____",1697768567626,536870920]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6531e478-f81a-4f35-bd98-4670f54c8bb1logseq____",536870932]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",56,536870920]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",56,536870920]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",56,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",56,536870920]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u6531e477-8fdd-422a-b0a8-486f6c822e66logseq____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Klogseq____",1697768567910,536870921]],[logseq____"^15logseq____",[59,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[59,logseq____"^Ylogseq____",logseq____"quadratische ergänzunglogseq____",536870921]],[logseq____"^15logseq____",[59,logseq____"^11logseq____",logseq____"Quadratische Ergänzunglogseq____",536870921]],[logseq____"^15logseq____",[59,logseq____"^Blogseq____",1697768567910,536870921]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u6531e477-fcf3-4c0b-81a8-9bc55bdf01ealogseq____",536870921]],[logseq____"^15logseq____",[60,logseq____"^Klogseq____",1697768567897,536870921]],[logseq____"^15logseq____",[60,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[60,logseq____"^Ylogseq____",logseq____"potenzenlogseq____",536870921]],[logseq____"^15logseq____",[60,logseq____"^11logseq____",logseq____"Potenzenlogseq____",536870921]],[logseq____"^15logseq____",[60,logseq____"^Blogseq____",1697768567897,536870921]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6531e477-6907-4ddd-8bc1-9154096ffdb3logseq____",536870921]],[logseq____"^15logseq____",[61,logseq____"^Klogseq____",1697768567894,536870921]],[logseq____"^15logseq____",[61,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[61,logseq____"^Ylogseq____",logseq____"pascalsches dreiecklogseq____",536870921]],[logseq____"^15logseq____",[61,logseq____"^11logseq____",logseq____"Pascalsches Dreiecklogseq____",536870921]],[logseq____"^15logseq____",[61,logseq____"^Blogseq____",1697768567894,536870921]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u6531e477-9e21-4a74-a707-063a98dd4d9flogseq____",536870921]],[logseq____"^15logseq____",[62,logseq____"^Klogseq____",1697768567908,536870921]],[logseq____"^15logseq____",[62,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[62,logseq____"^Ylogseq____",logseq____"quadratische gleichungenlogseq____",536870921]],[logseq____"^15logseq____",[62,logseq____"^11logseq____",logseq____"Quadratische Gleichungenlogseq____",536870921]],[logseq____"^15logseq____",[62,logseq____"^Blogseq____",1697768567908,536870921]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u6531e477-48e3-473d-90ad-73f659b7da66logseq____",536870921]],[logseq____"^15logseq____",[63,logseq____"^Klogseq____",1697768567912,536870921]],[logseq____"^15logseq____",[63,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[63,logseq____"^Ylogseq____",logseq____"wurzelgleichunglogseq____",536870921]],[logseq____"^15logseq____",[63,logseq____"^11logseq____",logseq____"Wurzelgleichunglogseq____",536870921]],[logseq____"^15logseq____",[63,logseq____"^Blogseq____",1697768567912,536870921]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6531e477-d743-4401-9178-11d618ff936dlogseq____",536870921]],[logseq____"^15logseq____",[64,logseq____"^Klogseq____",1697768567890,536870921]],[logseq____"^15logseq____",[64,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[64,logseq____"^Ylogseq____",logseq____"logarithmenlogseq____",536870921]],[logseq____"^15logseq____",[64,logseq____"^11logseq____",logseq____"Logarithmenlogseq____",536870921]],[logseq____"^15logseq____",[64,logseq____"^Blogseq____",1697768567890,536870921]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u6531e478-83cf-4985-98db-334fdeccd02alogseq____",536870926]],[logseq____"^15logseq____",[65,logseq____"^Klogseq____",1697768567896,536870921]],[logseq____"^15logseq____",[65,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[65,logseq____"^Ylogseq____",logseq____"binomialkoeffizientlogseq____",536870921]],[logseq____"^15logseq____",[65,logseq____"^11logseq____",logseq____"Binomialkoeffizientlogseq____",536870921]],[logseq____"^15logseq____",[65,logseq____"^Blogseq____",1697768567896,536870921]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6531e477-27ea-45b9-888f-46835b7d8c90logseq____",536870921]],[logseq____"^15logseq____",[66,logseq____"^Klogseq____",1697768567889,536870921]],[logseq____"^15logseq____",[66,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[66,logseq____"^Ylogseq____",logseq____"gleichungenlogseq____",536870921]],[logseq____"^15logseq____",[66,logseq____"^11logseq____",logseq____"Gleichungenlogseq____",536870921]],[logseq____"^15logseq____",[66,logseq____"^Blogseq____",1697768567889,536870921]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u6531e477-0b04-4f89-8aa2-96f2f8a86314logseq____",536870921]],[logseq____"^15logseq____",[67,logseq____"^Klogseq____",1697768567893,536870921]],[logseq____"^15logseq____",[67,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[67,logseq____"^Ylogseq____",logseq____"binomische formelnlogseq____",536870921]],[logseq____"^15logseq____",[67,logseq____"^11logseq____",logseq____"Binomische Formelnlogseq____",536870921]],[logseq____"^15logseq____",[67,logseq____"^Blogseq____",1697768567893,536870921]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u6531e477-e00d-48d4-a038-152beadb72e8logseq____",536870921]],[logseq____"^15logseq____",[68,logseq____"^Klogseq____",1697768567912,536870921]],[logseq____"^15logseq____",[68,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[68,logseq____"^Ylogseq____",logseq____"beispielelogseq____",536870921]],[logseq____"^15logseq____",[68,logseq____"^11logseq____",logseq____"Beispielelogseq____",536870921]],[logseq____"^15logseq____",[68,logseq____"^Blogseq____",1697768567912,536870921]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u6531e478-3f61-4d99-beb9-0ae56d2abbf9logseq____",536870925]],[logseq____"^15logseq____",[69,logseq____"^Klogseq____",1697768567892,536870921]],[logseq____"^15logseq____",[69,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[69,logseq____"^Ylogseq____",logseq____"trigonometrielogseq____",536870921]],[logseq____"^15logseq____",[69,logseq____"^11logseq____",logseq____"Trigonometrielogseq____",536870921]],[logseq____"^15logseq____",[69,logseq____"^Blogseq____",1697768567892,536870921]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u6531e477-8f00-4fc1-9d27-a85fef8c456clogseq____",536870921]],[logseq____"^15logseq____",[70,logseq____"^Klogseq____",1697768567899,536870921]],[logseq____"^15logseq____",[70,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[70,logseq____"^Ylogseq____",logseq____"wurzelnlogseq____",536870921]],[logseq____"^15logseq____",[70,logseq____"^11logseq____",logseq____"Wurzelnlogseq____",536870921]],[logseq____"^15logseq____",[70,logseq____"^Blogseq____",1697768567899,536870921]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u6531e477-f41f-422c-aede-af24ec600138logseq____",536870921]],[logseq____"^15logseq____",[71,logseq____"^Klogseq____",1697768567897,536870921]],[logseq____"^15logseq____",[71,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[71,logseq____"^Ylogseq____",logseq____"pascalsche dreiecklogseq____",536870921]],[logseq____"^15logseq____",[71,logseq____"^11logseq____",logseq____"Pascalsche Dreiecklogseq____",536870921]],[logseq____"^15logseq____",[71,logseq____"^Blogseq____",1697768567897,536870921]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u6531e477-c3aa-4698-a400-e0a9d1fc87c1logseq____",536870921]],[logseq____"^15logseq____",[72,logseq____"^Klogseq____",1697768567907,536870921]],[logseq____"^15logseq____",[72,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[72,logseq____"^Ylogseq____",logseq____"rationalmachenlogseq____",536870921]],[logseq____"^15logseq____",[72,logseq____"^11logseq____",logseq____"Rationalmachenlogseq____",536870921]],[logseq____"^15logseq____",[72,logseq____"^Blogseq____",1697768567907,536870921]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u6531e477-ef5a-4e98-a2cb-041228a0fe05logseq____",536870921]],[logseq____"^15logseq____",[73,logseq____"^Klogseq____",1697768567898,536870921]],[logseq____"^15logseq____",[73,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[73,logseq____"^Ylogseq____",logseq____"auffrischung mathematik/23-10-04logseq____",536870921]],[logseq____"^15logseq____",[73,logseq____"^Alogseq____",56,536870921]],[logseq____"^15logseq____",[73,logseq____"^11logseq____",logseq____"Auffrischung Mathematik/23-10-04logseq____",536870921]],[logseq____"^15logseq____",[73,logseq____"^Blogseq____",1697768567898,536870921]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u6531e477-22b7-43b7-9bd4-57f21818b59alogseq____",536870921]],[logseq____"^15logseq____",[74,logseq____"^Klogseq____",1697768567911,536870921]],[logseq____"^15logseq____",[74,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[74,logseq____"^Ylogseq____",logseq____"satz von vietalogseq____",536870921]],[logseq____"^15logseq____",[74,logseq____"^11logseq____",logseq____"Satz von Vietalogseq____",536870921]],[logseq____"^15logseq____",[74,logseq____"^Blogseq____",1697768567911,536870921]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u6531e477-84cc-4d1b-a1ab-4fa0490cd062logseq____",536870921]],[logseq____"^15logseq____",[75,logseq____"^Klogseq____",1697768567900,536870921]],[logseq____"^15logseq____",[75,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[75,logseq____"^Ylogseq____",logseq____"fixmelogseq____",536870921]],[logseq____"^15logseq____",[75,logseq____"^11logseq____",logseq____"FIXMElogseq____",536870921]],[logseq____"^15logseq____",[75,logseq____"^Blogseq____",1697768567900,536870921]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u6531e478-96a7-4f6c-a837-ec4bc1eb901blogseq____",536870925]],[logseq____"^15logseq____",[76,logseq____"^Klogseq____",1697768567910,536870921]],[logseq____"^15logseq____",[76,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[76,logseq____"^Ylogseq____",logseq____"pq-formellogseq____",536870921]],[logseq____"^15logseq____",[76,logseq____"^11logseq____",logseq____"pq-Formellogseq____",536870921]],[logseq____"^15logseq____",[76,logseq____"^Blogseq____",1697768567910,536870921]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u6531e477-05f0-4f90-9404-3a504b9da6c6logseq____",536870921]],[logseq____"^15logseq____",[77,logseq____"^Klogseq____",1697768567886,536870921]],[logseq____"^15logseq____",[77,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[77,logseq____"^Ylogseq____",logseq____"linkslogseq____",536870921]],[logseq____"^15logseq____",[77,logseq____"^11logseq____",logseq____"Linkslogseq____",536870921]],[logseq____"^15logseq____",[77,logseq____"^Blogseq____",1697768567886,536870921]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u6531e477-5e3b-4305-a27a-471c9cea344alogseq____",536870921]],[logseq____"^15logseq____",[78,logseq____"^Klogseq____",1697768567906,536870921]],[logseq____"^15logseq____",[78,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[78,logseq____"^Ylogseq____",logseq____"nennerlogseq____",536870921]],[logseq____"^15logseq____",[78,logseq____"^11logseq____",logseq____"Nennerlogseq____",536870921]],[logseq____"^15logseq____",[78,logseq____"^Blogseq____",1697768567906,536870921]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u6531e477-8ce2-45db-9362-2d1a07495a54logseq____",536870921]],[logseq____"^15logseq____",[79,logseq____"^Klogseq____",1697768567887,536870921]],[logseq____"^15logseq____",[79,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[79,logseq____"^Ylogseq____",logseq____"wolframalphalogseq____",536870921]],[logseq____"^15logseq____",[79,logseq____"^11logseq____",logseq____"Wolframalphalogseq____",536870921]],[logseq____"^15logseq____",[79,logseq____"^Blogseq____",1697768567887,536870921]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u6531e477-dfff-46dd-9bbd-f8a6598e01fblogseq____",536870921]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",106,536870921]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",106,536870921]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u6531e477-35f4-4557-85c1-e194f068ef27logseq____",536870921]],[logseq____"^15logseq____",[81,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(2x+y)^4logseq____&=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5logseq____&=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",91,536870921]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",91,536870921]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",61,536870921]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[81,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u6531e477-b354-4bf8-b197-24f03e2daadflogseq____",536870921]],[logseq____"^15logseq____",[82,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870921]],[logseq____"^15logseq____",[82,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[82,logseq____"^Flogseq____",89,536870921]],[logseq____"^15logseq____",[82,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[82,logseq____"^Vlogseq____",116,536870921]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",62,536870921]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[82,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",1],536870921]],[logseq____"^15logseq____",[82,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[82,logseq____"^Hlogseq____",62,536870921]],[logseq____"^15logseq____",[82,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u6531e477-7c7b-4396-9661-2fb17fbbc004logseq____",536870921]],[logseq____"^15logseq____",[83,logseq____"^Qlogseq____",logseq____"Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____",536870921]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",135,536870921]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",126,536870921]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",63,536870921]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u6531e477-6a96-4cce-9cdf-2321c8f5dc8dlogseq____",536870921]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870921]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",81,536870921]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",91,536870921]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",61,536870921]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",75,536870921]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",75,536870921]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u6531e477-43ea-4cff-9a3e-32eb6be3dd05logseq____",536870921]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870921]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",113,536870921]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",113,536870921]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",77,536870921]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",79,536870921]],[logseq____"^15logseq____",[85,logseq____"^Hlogseq____",79,536870921]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u6531e477-2300-4c9b-bc92-4d7bf347d741logseq____",536870921]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870921]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",91,536870921]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",111,536870921]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",61,536870921]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",65,536870921]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[86,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870921]],[logseq____"^15logseq____",[86,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[86,logseq____"^Hlogseq____",65,536870921]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u6531e477-5667-4b4f-b7ec-3d837bf53988logseq____",536870921]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",104,536870921]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",101,536870921]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",69,536870921]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u6531e477-5ae4-4fed-ba0f-f5a8c7d705d3logseq____",536870921]],[logseq____"^15logseq____",[88,logseq____"^Qlogseq____",logseq____"$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",92,536870921]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",92,536870921]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",72,536870921]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",78,536870921]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u6531e477-d169-4463-8408-60b97c280104logseq____",536870921]],[logseq____"^15logseq____",[89,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870921]],[logseq____"^15logseq____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",107,536870921]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",116,536870921]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[89,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[89,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[89,logseq____"^Hlogseq____",70,536870921]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u6531e477-ac77-4200-a756-1844e4ca1667logseq____",536870921]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&=a^2-b^2\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",102,536870921]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",102,536870921]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u6531e477-fc40-47fe-87e7-f573fe9f4236logseq____",536870921]],[logseq____"^15logseq____",[91,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870921]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",125,536870921]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",111,536870921]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",61,536870921]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[91,logseq____"^Hlogseq____",68,536870921]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u6531e477-dd26-4a5c-b564-debceb7a9c4dlogseq____",536870921]],[logseq____"^15logseq____",[92,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870921]],[logseq____"^15logseq____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",108,536870921]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",89,536870921]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",72,536870921]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",78,536870921]],[logseq____"^15logseq____",[92,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870921]],[logseq____"^15logseq____",[92,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[92,logseq____"^Hlogseq____",72,536870921]],[logseq____"^15logseq____",[92,logseq____"^Hlogseq____",78,536870921]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u6531e477-fb4d-4dcf-81a7-f0b73d53eb90logseq____",536870921]],[logseq____"^15logseq____",[93,logseq____"^Qlogseq____",logseq____"[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0 logseq____&logseq____& \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&=-p logseq____&logseq____& x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",112,536870921]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",62,536870921]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",74,536870921]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",76,536870921]],[logseq____"^15logseq____",[93,logseq____"^Hlogseq____",74,536870921]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u6531e477-38d0-4fc2-b392-e84af969f96flogseq____",536870921]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870921]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",87,536870921]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",87,536870921]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",69,536870921]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",75,536870921]],[logseq____"^15logseq____",[94,logseq____"^Hlogseq____",75,536870921]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u6531e477-5a61-4380-b880-be14381aed7flogseq____",536870921]],[logseq____"^15logseq____",[95,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870921]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",86,536870921]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",86,536870921]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",61,536870921]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",65,536870921]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",71,536870921]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[95,logseq____"^Hlogseq____",71,536870921]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u6531e477-bcd0-43a4-a975-faf0e58ad383logseq____",536870921]],[logseq____"^15logseq____",[96,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&= \\\\frac1{\\\\ln a}\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[96,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[96,logseq____"^Flogseq____",127,536870921]],[logseq____"^15logseq____",[96,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[96,logseq____"^Vlogseq____",118,536870921]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",64,536870921]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[96,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[96,logseq____"^;logseq____",logseq____"~u6531e477-a06e-4e4a-a0b9-e546f35a7c01logseq____",536870921]],[logseq____"^15logseq____",[97,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[97,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[97,logseq____"^Flogseq____",137,536870921]],[logseq____"^15logseq____",[97,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[97,logseq____"^Vlogseq____",124,536870921]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[97,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[97,logseq____"^;logseq____",logseq____"~u6531e477-7a76-4788-9dd5-249d7d93e1b3logseq____",536870921]],[logseq____"^15logseq____",[98,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nax^2+bx+clogseq____&=0logseq____&|:a\\\\quadlogseq____&a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&= 0\\\\\\\\\\nplogseq____&=\\\\frac ba,logseq____&q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&=0\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[98,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[98,logseq____"^Flogseq____",82,536870921]],[logseq____"^15logseq____",[98,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[98,logseq____"^Vlogseq____",82,536870921]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",62,536870921]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[98,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[98,logseq____"^;logseq____",logseq____"~u6531e477-72c7-4874-bbc4-c779ae8bc9dblogseq____",536870921]],[logseq____"^15logseq____",[99,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[99,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[99,logseq____"^Flogseq____",121,536870921]],[logseq____"^15logseq____",[99,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[99,logseq____"^Vlogseq____",109,536870921]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[99,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[99,logseq____"^;logseq____",logseq____"~u6531e477-bfd5-47ac-94ab-54bd689409eblogseq____",536870921]],[logseq____"^15logseq____",[100,logseq____"^Qlogseq____",logseq____"https://www.wolframalpha.comlogseq____",536870921]],[logseq____"^15logseq____",[100,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[100,logseq____"^Flogseq____",85,536870921]],[logseq____"^15logseq____",[100,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[100,logseq____"^Vlogseq____",85,536870921]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",77,536870921]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",79,536870921]],[logseq____"^15logseq____",[100,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[100,logseq____"^;logseq____",logseq____"~u6531e477-0646-4b51-aa80-c8f9623dc582logseq____",536870921]],[logseq____"^15logseq____",[101,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870921]],[logseq____"^15logseq____",[101,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[101,logseq____"^Flogseq____",106,536870921]],[logseq____"^15logseq____",[101,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[101,logseq____"^Vlogseq____",73,536870921]],[logseq____"^15logseq____",[101,logseq____"^Ulogseq____",69,536870921]],[logseq____"^15logseq____",[101,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[101,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[101,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[101,logseq____"^Hlogseq____",69,536870921]],[logseq____"^15logseq____",[101,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[101,logseq____"^;logseq____",logseq____"~u6531e477-5a2c-4453-8046-9016cb5b6782logseq____",536870921]],[logseq____"^15logseq____",[102,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870921]],[logseq____"^15logseq____",[102,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[102,logseq____"^Flogseq____",132,536870921]],[logseq____"^15logseq____",[102,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[102,logseq____"^Vlogseq____",107,536870921]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[102,logseq____"^Hlogseq____",68,536870921]],[logseq____"^15logseq____",[102,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[102,logseq____"^;logseq____",logseq____"~u6531e477-ad5e-49e8-adc6-07a0d47560a7logseq____",536870921]],[logseq____"^15logseq____",[103,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[103,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[103,logseq____"^Flogseq____",129,536870921]],[logseq____"^15logseq____",[103,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[103,logseq____"^Vlogseq____",128,536870921]],[logseq____"^15logseq____",[103,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[103,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[103,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[103,logseq____"^;logseq____",logseq____"~u6531e477-83e8-463d-8bc5-060e5adac348logseq____",536870921]],[logseq____"^15logseq____",[104,logseq____"^Qlogseq____",logseq____"$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[104,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[104,logseq____"^Flogseq____",101,536870921]],[logseq____"^15logseq____",[104,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[104,logseq____"^Vlogseq____",101,536870921]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",69,536870921]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[104,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[104,logseq____"^;logseq____",logseq____"~u6531e477-50e6-4075-9739-25c831f09885logseq____",536870921]],[logseq____"^15logseq____",[105,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&=x^2\\\\\\\\\\ny^2-34y+225logseq____&=0\\\\\\\\\\ny_{1,2}logseq____&=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&\\\\rightarrow logseq____&x_1=5;logseq____&x_2=-5\\\\\\\\\\nx^2=9logseq____&\\\\rightarrow logseq____&x_1=3;logseq____&x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[105,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[105,logseq____"^Flogseq____",93,536870921]],[logseq____"^15logseq____",[105,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[105,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",62,536870921]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",76,536870921]],[logseq____"^15logseq____",[105,logseq____"^Hlogseq____",68,536870921]],[logseq____"^15logseq____",[105,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[105,logseq____"^;logseq____",logseq____"~u6531e477-834d-4cc2-86ec-8b3a6379807clogseq____",536870921]],[logseq____"^15logseq____",[106,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870921]],[logseq____"^15logseq____",[106,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[106,logseq____"^Flogseq____",124,536870921]],[logseq____"^15logseq____",[106,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[106,logseq____"^Vlogseq____",73,536870921]],[logseq____"^15logseq____",[106,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[106,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[106,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[106,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[106,logseq____"^;logseq____",logseq____"~u6531e477-d878-49b8-b620-62b54f755afelogseq____",536870921]],[logseq____"^15logseq____",[107,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870921]],[logseq____"^15logseq____",[107,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[107,logseq____"^Flogseq____",116,536870921]],[logseq____"^15logseq____",[107,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[107,logseq____"^Vlogseq____",116,536870921]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[107,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[107,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[107,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[107,logseq____"^Hlogseq____",60,536870921]],[logseq____"^15logseq____",[107,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[107,logseq____"^;logseq____",logseq____"~u6531e477-c202-43df-bbcf-f8e4f2e2e975logseq____",536870921]],[logseq____"^15logseq____",[108,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[108,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[108,logseq____"^Flogseq____",114,536870921]],[logseq____"^15logseq____",[108,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[108,logseq____"^Vlogseq____",89,536870921]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[108,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[108,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[108,logseq____"^;logseq____",logseq____"~u6531e477-5db9-401d-9f73-7ddfe89129a9logseq____",536870921]],[logseq____"^15logseq____",[109,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870921]],[logseq____"^15logseq____",[109,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[109,logseq____"^Flogseq____",113,536870921]],[logseq____"^15logseq____",[109,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[109,logseq____"^Vlogseq____",73,536870921]],[logseq____"^15logseq____",[109,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[109,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[109,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[109,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[109,logseq____"^Hlogseq____",60,536870921]],[logseq____"^15logseq____",[109,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[109,logseq____"^;logseq____",logseq____"~u6531e477-de49-4744-b796-1cc4b33077d2logseq____",536870921]],[logseq____"^15logseq____",[110,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870921]],[logseq____"^15logseq____",[110,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[110,logseq____"^Flogseq____",133,536870921]],[logseq____"^15logseq____",[110,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[110,logseq____"^Vlogseq____",133,536870921]],[logseq____"^15logseq____",[110,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[110,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[110,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[110,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[110,logseq____"^;logseq____",logseq____"~u6531e477-8ce7-4334-a4d3-8963f2c60a35logseq____",536870921]],[logseq____"^15logseq____",[111,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870921]],[logseq____"^15logseq____",[111,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[111,logseq____"^Flogseq____",103,536870921]],[logseq____"^15logseq____",[111,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[111,logseq____"^Vlogseq____",128,536870921]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",61,536870921]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[111,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[111,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870921]],[logseq____"^15logseq____",[111,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[111,logseq____"^Hlogseq____",61,536870921]],[logseq____"^15logseq____",[111,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[111,logseq____"^;logseq____",logseq____"~u6531e477-a3f0-46e0-88b2-a6df3e7d4366logseq____",536870921]],[logseq____"^15logseq____",[112,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[112,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[112,logseq____"^Flogseq____",120,536870921]],[logseq____"^15logseq____",[112,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[112,logseq____"^Vlogseq____",120,536870921]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",59,536870921]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",62,536870921]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[112,logseq____"^Ulogseq____",76,536870921]],[logseq____"^15logseq____",[112,logseq____"^Hlogseq____",59,536870921]],[logseq____"^15logseq____",[112,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[112,logseq____"^;logseq____",logseq____"~u6531e477-39c8-42f0-81c3-517eb0e85e42logseq____",536870921]],[logseq____"^15logseq____",[113,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870921]],[logseq____"^15logseq____",[113,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[113,logseq____"^Flogseq____",73,536870921]],[logseq____"^15logseq____",[113,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[113,logseq____"^Vlogseq____",73,536870921]],[logseq____"^15logseq____",[113,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[113,logseq____"^Ulogseq____",77,536870921]],[logseq____"^15logseq____",[113,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[113,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[113,logseq____"^Hlogseq____",77,536870921]],[logseq____"^15logseq____",[113,logseq____"^17logseq____",false,536870921]],[logseq____"^15logseq____",[113,logseq____"^;logseq____",logseq____"~u6531e477-a83a-4727-9c44-9a8cd8a67a04logseq____",536870921]],[logseq____"^15logseq____",[114,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870921]],[logseq____"^15logseq____",[114,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[114,logseq____"^Flogseq____",123,536870921]],[logseq____"^15logseq____",[114,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[114,logseq____"^Vlogseq____",89,536870921]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[114,logseq____"^Hlogseq____",68,536870921]],[logseq____"^15logseq____",[114,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[114,logseq____"^;logseq____",logseq____"~u6531e477-80b7-4c7b-bb25-bbceabbfa0bblogseq____",536870921]],[logseq____"^15logseq____",[115,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870921]],[logseq____"^15logseq____",[115,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[115,logseq____"^Flogseq____",93,536870921]],[logseq____"^15logseq____",[115,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[115,logseq____"^Vlogseq____",93,536870921]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",62,536870921]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",74,536870921]],[logseq____"^15logseq____",[115,logseq____"^Ulogseq____",76,536870921]],[logseq____"^15logseq____",[115,logseq____"^Hlogseq____",68,536870921]],[logseq____"^15logseq____",[115,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[115,logseq____"^;logseq____",logseq____"~u6531e477-a8a3-4850-8871-ea033719b0eblogseq____",536870921]],[logseq____"^15logseq____",[116,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870921]],[logseq____"^15logseq____",[116,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[116,logseq____"^Flogseq____",128,536870921]],[logseq____"^15logseq____",[116,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[116,logseq____"^Vlogseq____",73,536870921]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[116,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[116,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[116,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[116,logseq____"^Hlogseq____",60,536870921]],[logseq____"^15logseq____",[116,logseq____"^Hlogseq____",70,536870921]],[logseq____"^15logseq____",[116,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[116,logseq____"^;logseq____",logseq____"~u6531e477-5dbf-4771-9883-43dbaa39d0a2logseq____",536870921]],[logseq____"^15logseq____",[117,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870921]],[logseq____"^15logseq____",[117,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[117,logseq____"^Flogseq____",89,536870921]],[logseq____"^15logseq____",[117,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[117,logseq____"^Vlogseq____",89,536870921]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[117,logseq____"^Ulogseq____",75,536870921]],[logseq____"^15logseq____",[117,logseq____"^Hlogseq____",75,536870921]],[logseq____"^15logseq____",[117,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[117,logseq____"^;logseq____",logseq____"~u6531e477-8f47-49b1-93a3-03a9aece7baalogseq____",536870921]],[logseq____"^15logseq____",[118,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870921]],[logseq____"^15logseq____",[118,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[118,logseq____"^Flogseq____",109,536870921]],[logseq____"^15logseq____",[118,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[118,logseq____"^Vlogseq____",73,536870921]],[logseq____"^15logseq____",[118,logseq____"^Ulogseq____",64,536870921]],[logseq____"^15logseq____",[118,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[118,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[118,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[118,logseq____"^Hlogseq____",64,536870921]],[logseq____"^15logseq____",[118,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[118,logseq____"^;logseq____",logseq____"~u6531e477-728e-4f61-a770-f633125bb1d6logseq____",536870921]],[logseq____"^15logseq____",[119,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870921]],[logseq____"^15logseq____",[119,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[119,logseq____"^Flogseq____",130,536870921]],[logseq____"^15logseq____",[119,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[119,logseq____"^Vlogseq____",114,536870921]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",75,536870921]],[logseq____"^15logseq____",[119,logseq____"^Hlogseq____",75,536870921]],[logseq____"^15logseq____",[119,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[119,logseq____"^;logseq____",logseq____"~u6531e477-265f-414e-967a-35363877351flogseq____",536870921]],[logseq____"^15logseq____",[120,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870921]],[logseq____"^15logseq____",[120,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[120,logseq____"^Flogseq____",98,536870921]],[logseq____"^15logseq____",[120,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[120,logseq____"^Vlogseq____",82,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",62,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",76,536870921]],[logseq____"^15logseq____",[120,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870921]],[logseq____"^15logseq____",[120,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[120,logseq____"^Hlogseq____",76,536870921]],[logseq____"^15logseq____",[120,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[120,logseq____"^;logseq____",logseq____"~u6531e477-5866-4158-9114-e38d51245418logseq____",536870921]],[logseq____"^15logseq____",[121,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[121,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[121,logseq____"^Flogseq____",109,536870921]],[logseq____"^15logseq____",[121,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[121,logseq____"^Vlogseq____",109,536870921]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",66,536870921]],[logseq____"^15logseq____",[121,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[121,logseq____"^Hlogseq____",66,536870921]],[logseq____"^15logseq____",[121,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[121,logseq____"^;logseq____",logseq____"~u6531e477-4da2-4a29-b840-92b6f445b32elogseq____",536870921]],[logseq____"^15logseq____",[122,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&= p logseq____&, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&=0\\\\\\\\\\nx^2-7x+12logseq____&=0\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[122,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[122,logseq____"^Flogseq____",115,536870921]],[logseq____"^15logseq____",[122,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[122,logseq____"^Vlogseq____",115,536870921]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",62,536870921]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",74,536870921]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",76,536870921]],[logseq____"^15logseq____",[122,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[122,logseq____"^;logseq____",logseq____"~u6531e477-3d4c-4577-adcc-4291711a5141logseq____",536870921]],[logseq____"^15logseq____",[123,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[123,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[123,logseq____"^Flogseq____",117,536870921]],[logseq____"^15logseq____",[123,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[123,logseq____"^Vlogseq____",89,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[123,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[123,logseq____"^;logseq____",logseq____"~u6531e477-2437-456b-a11d-73eeb79eac3blogseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^Flogseq____",118,536870921]],[logseq____"^15logseq____",[124,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[124,logseq____"^Vlogseq____",73,536870921]],[logseq____"^15logseq____",[124,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[124,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[124,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[124,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[124,logseq____"^Hlogseq____",70,536870921]],[logseq____"^15logseq____",[124,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[124,logseq____"^;logseq____",logseq____"~u6531e477-4467-48a3-a46a-02981adc75d2logseq____",536870921]],[logseq____"^15logseq____",[125,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c} (a+b)^0logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 \\\\\\\\\\n(a+b)^1logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^2logseq____&logseq____&logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 2 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^3logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 3 logseq____&logseq____& 3 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^4logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 4 logseq____&logseq____& 6 logseq____&logseq____& 4 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^5logseq____&logseq____&logseq____& 1 logseq____&logseq____& 5 logseq____&logseq____& 10 logseq____&logseq____& 10 logseq____&logseq____& 5 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^6logseq____&logseq____& 1 logseq____&logseq____& 6 logseq____&logseq____& 15 logseq____&logseq____& 20 logseq____&logseq____& 15 logseq____&logseq____& 6 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^7logseq____&1 logseq____&logseq____& 7 logseq____&logseq____&21 logseq____&logseq____& 35 logseq____&logseq____& 35 logseq____&logseq____& \\\\cdots\\\\end{array}logseq____",536870921]],[logseq____"^15logseq____",[125,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[125,logseq____"^Flogseq____",111,536870921]],[logseq____"^15logseq____",[125,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[125,logseq____"^Vlogseq____",111,536870921]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",61,536870921]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[125,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[125,logseq____"^;logseq____",logseq____"~u6531e477-fccf-4ef9-ab7e-33d878820187logseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Qlogseq____",logseq____"# [[Wurzelgleichung]]logseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Flogseq____",82,536870921]],[logseq____"^15logseq____",[126,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[126,logseq____"^Vlogseq____",116,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",63,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[126,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[126,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[126,logseq____"^Hlogseq____",63,536870921]],[logseq____"^15logseq____",[126,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[126,logseq____"^;logseq____",logseq____"~u6531e477-f2ed-4ca6-a74e-4bf8dd992968logseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Flogseq____",118,536870921]],[logseq____"^15logseq____",[127,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[127,logseq____"^Vlogseq____",118,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",64,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[127,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[127,logseq____"^;logseq____",logseq____"~u6531e477-807f-49f9-828c-fd031ff4edb1logseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Flogseq____",101,536870921]],[logseq____"^15logseq____",[128,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[128,logseq____"^Vlogseq____",73,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[128,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870921]],[logseq____"^15logseq____",[128,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[128,logseq____"^Hlogseq____",67,536870921]],[logseq____"^15logseq____",[128,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[128,logseq____"^;logseq____",logseq____"~u6531e477-9c72-44cf-b570-51dfa85556fblogseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&=a^2+2ab+b^2logseq____&,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&=a^2-2ab+b^2logseq____&,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&=a^2-b^2logseq____&,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Flogseq____",128,536870921]],[logseq____"^15logseq____",[129,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[129,logseq____"^Vlogseq____",128,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[129,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[129,logseq____"^;logseq____",logseq____"~u6531e477-5e68-46d8-a8be-8a3d4d93115blogseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{y^2}=\\\\left|y\\\\right|\\\\\\\\\\n\\\\sqrt[5]{a\\\\sqrt[3]a}=\\\\sqrt[5]{\\\\sqrt[3]{a^3}\\\\sqrt[3]a}\\nlogseq____&=\\\\sqrt[5]{\\\\sqrt[3]{a^4}}\\n=\\\\sqrt[5]{a^\\\\frac43}\\n=a^{\\\\frac43\\\\frac15}=a^\\\\frac4{15}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Flogseq____",114,536870921]],[logseq____"^15logseq____",[130,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[130,logseq____"^Vlogseq____",114,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[130,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[130,logseq____"^;logseq____",logseq____"~u6531e477-8db7-488b-bc5e-a93b5c6bdcfelogseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&, a,b,logseq____>0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Flogseq____",134,536870921]],[logseq____"^15logseq____",[131,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[131,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",72,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",78,536870921]],[logseq____"^15logseq____",[131,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[131,logseq____"^;logseq____",logseq____"~u6531e477-c04f-4cc1-a5c8-0ad8f8df0a93logseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\na^nlogseq____&=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____& a,blogseq____>0\\\\\\\\\\na^2b^2logseq____&=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&=a^{nm}\\\\\\\\\\na^0logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Flogseq____",107,536870921]],[logseq____"^15logseq____",[132,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[132,logseq____"^Vlogseq____",107,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[132,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[132,logseq____"^;logseq____",logseq____"~u6531e477-f544-4ef8-b3c4-e51e993678b2logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Flogseq____",102,536870921]],[logseq____"^15logseq____",[133,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[133,logseq____"^Vlogseq____",107,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[133,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[133,logseq____"^;logseq____",logseq____"~u6531e477-cfcd-4b79-9794-edb01b374a01logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Flogseq____",88,536870921]],[logseq____"^15logseq____",[134,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[134,logseq____"^Vlogseq____",92,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",68,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",72,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",78,536870921]],[logseq____"^15logseq____",[134,logseq____"^Hlogseq____",68,536870921]],[logseq____"^15logseq____",[134,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[134,logseq____"^;logseq____",logseq____"~u6531e477-0f2a-4f83-afc5-ef712eb355f7logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{a+5}-\\\\sqrt{x+3}logseq____&=2\\\\sqrt(x+1) logseq____&|logseq____&()^2\\\\\\\\\\n\\\\left(\\\\sqrt{x+5}-\\\\sqrt{x+3}\\\\right)^2logseq____&=4(x+1)\\\\\\\\\\n(x+5)-2\\\\sqrt{x+5}\\\\sqrt{x+3}+(x+3)logseq____&=4x+4logseq____&|logseq____&-(2x+8)\\\\\\\\\\n-2\\\\sqrt{(x+5)(x+3)}logseq____&=2x-4 logseq____&|logseq____&()^2\\\\\\\\\\n4(x+5)(x+3)logseq____&=4x^2-16x+16\\\\\\\\\\n4x^2+32x+60logseq____&=4x^2-16x+16logseq____&|logseq____&-4x^2+16x-16\\\\\\\\\\n48x+44logseq____&=0\\\\quad x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Flogseq____",126,536870921]],[logseq____"^15logseq____",[135,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[135,logseq____"^Vlogseq____",126,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",60,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",63,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[135,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[135,logseq____"^;logseq____",logseq____"~u6531e477-b460-465d-9699-10053b63f9aclogseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Flogseq____",95,536870921]],[logseq____"^15logseq____",[136,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[136,logseq____"^Vlogseq____",86,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",61,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",65,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",67,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[136,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[136,logseq____"^;logseq____",logseq____"~u6531e477-bb0b-4590-b478-8e65d91b80dblogseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Flogseq____",124,536870921]],[logseq____"^15logseq____",[137,logseq____"^Xlogseq____",73,536870921]],[logseq____"^15logseq____",[137,logseq____"^Vlogseq____",124,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",70,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",73,536870921]],[logseq____"^15logseq____",[137,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[137,logseq____"^;logseq____",logseq____"~u6531e477-f926-4486-bc10-593acc9d766blogseq____",536870921]],[logseq____"^15logseq____",[139,logseq____"^Klogseq____",1697768568259,536870922]],[logseq____"^15logseq____",[139,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[139,logseq____"^Ylogseq____",logseq____"kreislogseq____",536870922]],[logseq____"^15logseq____",[139,logseq____"^11logseq____",logseq____"Kreislogseq____",536870922]],[logseq____"^15logseq____",[139,logseq____"^Blogseq____",1697768568259,536870922]],[logseq____"^15logseq____",[139,logseq____"^;logseq____",logseq____"~u6531e478-fefa-4e6c-a39f-58e4364d499alogseq____",536870922]],[logseq____"^15logseq____",[140,logseq____"^Klogseq____",1697768568264,536870922]],[logseq____"^15logseq____",[140,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[140,logseq____"^Ylogseq____",logseq____"fester punktlogseq____",536870922]],[logseq____"^15logseq____",[140,logseq____"^11logseq____",logseq____"Fester Punktlogseq____",536870922]],[logseq____"^15logseq____",[140,logseq____"^Blogseq____",1697768568264,536870922]],[logseq____"^15logseq____",[140,logseq____"^;logseq____",logseq____"~u6531e478-cf31-41f3-b7c5-05659d6d6745logseq____",536870922]],[logseq____"^15logseq____",[141,logseq____"^Klogseq____",1697768568260,536870922]],[logseq____"^15logseq____",[141,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[141,logseq____"^Ylogseq____",logseq____"radiuslogseq____",536870922]],[logseq____"^15logseq____",[141,logseq____"^11logseq____",logseq____"Radiuslogseq____",536870922]],[logseq____"^15logseq____",[141,logseq____"^Blogseq____",1697768568260,536870922]],[logseq____"^15logseq____",[141,logseq____"^;logseq____",logseq____"~u6531e478-d9e7-4d9c-8d0f-06efc8dab757logseq____",536870922]],[logseq____"^15logseq____",[142,logseq____"^Klogseq____",1697768568256,536870922]],[logseq____"^15logseq____",[142,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[142,logseq____"^Ylogseq____",logseq____"fallunterscheidunglogseq____",536870922]],[logseq____"^15logseq____",[142,logseq____"^11logseq____",logseq____"Fallunterscheidunglogseq____",536870922]],[logseq____"^15logseq____",[142,logseq____"^Blogseq____",1697768568256,536870922]],[logseq____"^15logseq____",[142,logseq____"^;logseq____",logseq____"~u6531e478-2ed9-4c98-aeb0-fd60a998ba83logseq____",536870922]],[logseq____"^15logseq____",[143,logseq____"^Klogseq____",1697768568267,536870922]],[logseq____"^15logseq____",[143,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[143,logseq____"^Ylogseq____",logseq____"ellipselogseq____",536870922]],[logseq____"^15logseq____",[143,logseq____"^11logseq____",logseq____"Ellipselogseq____",536870922]],[logseq____"^15logseq____",[143,logseq____"^Blogseq____",1697768568267,536870922]],[logseq____"^15logseq____",[143,logseq____"^;logseq____",logseq____"~u6531e478-448f-4430-86f5-0ebbc3d921cflogseq____",536870922]],[logseq____"^15logseq____",[144,logseq____"^Klogseq____",1697768568259,536870922]],[logseq____"^15logseq____",[144,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[144,logseq____"^Ylogseq____",logseq____"mittelpunktlogseq____",536870922]],[logseq____"^15logseq____",[144,logseq____"^11logseq____",logseq____"Mittelpunktlogseq____",536870922]],[logseq____"^15logseq____",[144,logseq____"^Blogseq____",1697768568259,536870922]],[logseq____"^15logseq____",[144,logseq____"^;logseq____",logseq____"~u6531e478-6b77-4ee0-b2fa-a5bd0a347c58logseq____",536870922]],[logseq____"^15logseq____",[145,logseq____"^Klogseq____",1697768568263,536870922]],[logseq____"^15logseq____",[145,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[145,logseq____"^Ylogseq____",logseq____"konstantlogseq____",536870922]],[logseq____"^15logseq____",[145,logseq____"^11logseq____",logseq____"konstantlogseq____",536870922]],[logseq____"^15logseq____",[145,logseq____"^Blogseq____",1697768568263,536870922]],[logseq____"^15logseq____",[145,logseq____"^;logseq____",logseq____"~u6531e478-0964-4cfe-89df-7a4ac4989463logseq____",536870922]],[logseq____"^15logseq____",[146,logseq____"^Klogseq____",1697768568254,536870922]],[logseq____"^15logseq____",[146,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[146,logseq____"^Ylogseq____",logseq____"ungleichungenlogseq____",536870922]],[logseq____"^15logseq____",[146,logseq____"^11logseq____",logseq____"Ungleichungenlogseq____",536870922]],[logseq____"^15logseq____",[146,logseq____"^Blogseq____",1697768568254,536870922]],[logseq____"^15logseq____",[146,logseq____"^;logseq____",logseq____"~u6531e478-60a1-453b-b6b3-0bb0d2e53e44logseq____",536870931]],[logseq____"^15logseq____",[147,logseq____"^Klogseq____",1697768568264,536870922]],[logseq____"^15logseq____",[147,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[147,logseq____"^Ylogseq____",logseq____"brennpunktlogseq____",536870922]],[logseq____"^15logseq____",[147,logseq____"^11logseq____",logseq____"Brennpunktlogseq____",536870922]],[logseq____"^15logseq____",[147,logseq____"^Blogseq____",1697768568264,536870922]],[logseq____"^15logseq____",[147,logseq____"^;logseq____",logseq____"~u6531e478-7fde-49f0-9e60-028ab7a9669dlogseq____",536870922]],[logseq____"^15logseq____",[148,logseq____"^Klogseq____",1697768568267,536870922]],[logseq____"^15logseq____",[148,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[148,logseq____"^Ylogseq____",logseq____"asymptotelogseq____",536870922]],[logseq____"^15logseq____",[148,logseq____"^11logseq____",logseq____"Asymptotelogseq____",536870922]],[logseq____"^15logseq____",[148,logseq____"^Blogseq____",1697768568267,536870922]],[logseq____"^15logseq____",[148,logseq____"^;logseq____",logseq____"~u6531e478-d3b8-46a5-9d1d-7a00c975fa4clogseq____",536870922]],[logseq____"^15logseq____",[149,logseq____"^Klogseq____",1697768568251,536870922]],[logseq____"^15logseq____",[149,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[149,logseq____"^Ylogseq____",logseq____"lösungsmengenlogseq____",536870922]],[logseq____"^15logseq____",[149,logseq____"^11logseq____",logseq____"Lösungsmengenlogseq____",536870922]],[logseq____"^15logseq____",[149,logseq____"^Blogseq____",1697768568251,536870922]],[logseq____"^15logseq____",[149,logseq____"^;logseq____",logseq____"~u6531e478-b728-44df-b26e-37ec1ed8fa34logseq____",536870922]],[logseq____"^15logseq____",[150,logseq____"^Klogseq____",1697768568264,536870922]],[logseq____"^15logseq____",[150,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[150,logseq____"^Ylogseq____",logseq____"abstandlogseq____",536870922]],[logseq____"^15logseq____",[150,logseq____"^11logseq____",logseq____"Abstandlogseq____",536870922]],[logseq____"^15logseq____",[150,logseq____"^Blogseq____",1697768568264,536870922]],[logseq____"^15logseq____",[150,logseq____"^;logseq____",logseq____"~u6531e478-6c30-4474-8ab1-1a5a37525c74logseq____",536870922]],[logseq____"^15logseq____",[151,logseq____"^Klogseq____",1697768568267,536870922]],[logseq____"^15logseq____",[151,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[151,logseq____"^Ylogseq____",logseq____"hyperbellogseq____",536870922]],[logseq____"^15logseq____",[151,logseq____"^11logseq____",logseq____"Hyperbellogseq____",536870922]],[logseq____"^15logseq____",[151,logseq____"^Blogseq____",1697768568267,536870922]],[logseq____"^15logseq____",[151,logseq____"^;logseq____",logseq____"~u6531e478-17f7-45fd-b1ae-477fdd9cb4cflogseq____",536870922]],[logseq____"^15logseq____",[152,logseq____"^Klogseq____",1697768568267,536870922]],[logseq____"^15logseq____",[152,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[152,logseq____"^Ylogseq____",logseq____"summelogseq____",536870922]],[logseq____"^15logseq____",[152,logseq____"^11logseq____",logseq____"Summelogseq____",536870922]],[logseq____"^15logseq____",[152,logseq____"^Blogseq____",1697768568267,536870922]],[logseq____"^15logseq____",[152,logseq____"^;logseq____",logseq____"~u6531e478-d5dd-4b28-b880-f5c51a53982elogseq____",536870922]],[logseq____"^15logseq____",[153,logseq____"^Klogseq____",1697768568255,536870922]],[logseq____"^15logseq____",[153,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[153,logseq____"^Ylogseq____",logseq____"betraglogseq____",536870922]],[logseq____"^15logseq____",[153,logseq____"^11logseq____",logseq____"Betraglogseq____",536870922]],[logseq____"^15logseq____",[153,logseq____"^Blogseq____",1697768568255,536870922]],[logseq____"^15logseq____",[153,logseq____"^;logseq____",logseq____"~u6531e478-fb1d-42a8-9383-1a2316ca2d0dlogseq____",536870922]],[logseq____"^15logseq____",[154,logseq____"^Klogseq____",1697768568257,536870922]],[logseq____"^15logseq____",[154,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[154,logseq____"^Ylogseq____",logseq____"auffrischung mathematik/23-10-05logseq____",536870922]],[logseq____"^15logseq____",[154,logseq____"^Alogseq____",56,536870922]],[logseq____"^15logseq____",[154,logseq____"^11logseq____",logseq____"Auffrischung Mathematik/23-10-05logseq____",536870922]],[logseq____"^15logseq____",[154,logseq____"^Blogseq____",1697768568257,536870922]],[logseq____"^15logseq____",[154,logseq____"^;logseq____",logseq____"~u6531e478-788b-4630-9ab4-bc6426a1774clogseq____",536870922]],[logseq____"^15logseq____",[155,logseq____"^Klogseq____",1697768568266,536870922]],[logseq____"^15logseq____",[155,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[155,logseq____"^Ylogseq____",logseq____"differenzlogseq____",536870922]],[logseq____"^15logseq____",[155,logseq____"^11logseq____",logseq____"Differenzlogseq____",536870922]],[logseq____"^15logseq____",[155,logseq____"^Blogseq____",1697768568266,536870922]],[logseq____"^15logseq____",[155,logseq____"^;logseq____",logseq____"~u6531e478-75cc-4573-83ca-321e44a0c164logseq____",536870922]],[logseq____"^15logseq____",[156,logseq____"^Klogseq____",1697768568254,536870922]],[logseq____"^15logseq____",[156,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[156,logseq____"^Ylogseq____",logseq____"betragsungleichungenlogseq____",536870922]],[logseq____"^15logseq____",[156,logseq____"^11logseq____",logseq____"Betragsungleichungenlogseq____",536870922]],[logseq____"^15logseq____",[156,logseq____"^Blogseq____",1697768568254,536870922]],[logseq____"^15logseq____",[156,logseq____"^;logseq____",logseq____"~u6531e478-3a92-4434-b991-cee43275bb58logseq____",536870922]],[logseq____"^15logseq____",[157,logseq____"^Klogseq____",1697768568265,536870922]],[logseq____"^15logseq____",[157,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[157,logseq____"^Ylogseq____",logseq____"punktelogseq____",536870922]],[logseq____"^15logseq____",[157,logseq____"^11logseq____",logseq____"Punktelogseq____",536870922]],[logseq____"^15logseq____",[157,logseq____"^Blogseq____",1697768568265,536870922]],[logseq____"^15logseq____",[157,logseq____"^;logseq____",logseq____"~u6531e478-a2c1-48d6-ac5e-5696459c07ablogseq____",536870922]],[logseq____"^15logseq____",[158,logseq____"^Klogseq____",1697768568265,536870922]],[logseq____"^15logseq____",[158,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[158,logseq____"^Ylogseq____",logseq____"ebenenlogseq____",536870922]],[logseq____"^15logseq____",[158,logseq____"^11logseq____",logseq____"Ebenenlogseq____",536870922]],[logseq____"^15logseq____",[158,logseq____"^Blogseq____",1697768568265,536870922]],[logseq____"^15logseq____",[158,logseq____"^;logseq____",logseq____"~u6531e478-b560-4228-8d8e-4de5137ae67elogseq____",536870922]],[logseq____"^15logseq____",[159,logseq____"^Klogseq____",1697768568265,536870922]],[logseq____"^15logseq____",[159,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[159,logseq____"^Ylogseq____",logseq____"mengenlogseq____",536870922]],[logseq____"^15logseq____",[159,logseq____"^11logseq____",logseq____"Mengenlogseq____",536870922]],[logseq____"^15logseq____",[159,logseq____"^Blogseq____",1697768568265,536870922]],[logseq____"^15logseq____",[159,logseq____"^;logseq____",logseq____"~u6531e478-7e2c-48b3-8b9f-c5a986d00cfclogseq____",536870922]],[logseq____"^15logseq____",[160,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2}\\\\quad xlogseq____<3$\\n\\\\begin{align}\\n|\\\\underbrace{x-3}_{logseq____<0}|logseq____&=6(x-3)=-x+3\\\\\\\\\\n-x+3logseq____&\\\\le|x+2|\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[160,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[160,logseq____"^Flogseq____",206,536870922]],[logseq____"^15logseq____",[160,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[160,logseq____"^Vlogseq____",166,536870922]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[160,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[160,logseq____"^;logseq____",logseq____"~u6531e478-3f27-4a4c-aaba-28720c5f1073logseq____",536870922]],[logseq____"^15logseq____",[161,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup L_2=[3,\\\\infty)\\\\cup\\\\left[\\\\frac12,3\\\\right)=\\\\left[\\\\frac12,\\\\infty\\\\right)\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[161,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[161,logseq____"^Flogseq____",185,536870922]],[logseq____"^15logseq____",[161,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[161,logseq____"^Vlogseq____",166,536870922]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[161,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[161,logseq____"^;logseq____",logseq____"~u6531e478-25ba-4831-8435-51f39952beb8logseq____",536870922]],[logseq____"^15logseq____",[162,logseq____"^Qlogseq____",logseq____"logseq____",536870922]],[logseq____"^15logseq____",[162,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[162,logseq____"^Flogseq____",174,536870922]],[logseq____"^15logseq____",[162,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[162,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[162,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[162,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[162,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[162,logseq____"^;logseq____",logseq____"~u6531e478-b337-4851-8d15-518d79b48d4blogseq____",536870922]],[logseq____"^15logseq____",[163,logseq____"^Qlogseq____",logseq____"**oder** $\\\\rightarrow$ 5 ist abstand von x zu -3logseq____",536870922]],[logseq____"^15logseq____",[163,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[163,logseq____"^Flogseq____",216,536870922]],[logseq____"^15logseq____",[163,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[163,logseq____"^Vlogseq____",167,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[163,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[163,logseq____"^;logseq____",logseq____"~u6531e478-938f-45d4-9cd8-fce473f0e950logseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1a}\\\\quad x\\\\ge -2$\\n\\\\begin{align}\\n|x+2|logseq____&=x+2\\\\\\\\\\nx-3logseq____&\\\\le x+2 logseq____&|logseq____&+3-x\\\\\\\\\\n0logseq____&\\\\le5\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3,x\\\\ge-2,0\\\\le5\\\\right\\\\}=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3\\\\right\\\\}=[3,\\\\infty)\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[164,logseq____"^Flogseq____",172,536870922]],[logseq____"^15logseq____",[164,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[164,logseq____"^Vlogseq____",166,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[164,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[164,logseq____"^;logseq____",logseq____"~u6531e478-36d6-47d4-a3be-9bed3dfb4dealogseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Qlogseq____",logseq____"$\\\\text{Lösungsmenge der Gleichung }x^2+\\\\underbrace{4}_p x-\\\\underbrace{12}_q=0$\\n\\\\begin{align}\\nx_{1,2}logseq____&=\\\\frac{-p}2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\nlogseq____&=-2\\\\pm\\\\sqrt{\\\\frac{16}4-(-12)}\\\\\\\\\\nlogseq____&=-2\\\\pm4\\\\\\\\\\nLlogseq____&=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_\\\\text{Name}\\\\middle|\\\\underbrace{x^2+4x-12=0}_\\\\text{Eigenschaft}\\\\right\\\\}\\\\\\\\\\nLlogseq____&=\\\\left\\\\{2,-6\\\\right\\\\}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[165,logseq____"^Flogseq____",202,536870922]],[logseq____"^15logseq____",[165,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[165,logseq____"^Vlogseq____",202,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",149,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[165,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[165,logseq____"^;logseq____",logseq____"~u6531e478-0922-4b6d-b897-0dd7681e2915logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Qlogseq____",logseq____"### Lösung mit [[Fallunterscheidung]]logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[166,logseq____"^Flogseq____",200,536870922]],[logseq____"^15logseq____",[166,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[166,logseq____"^Vlogseq____",200,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[166,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870922]],[logseq____"^15logseq____",[166,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[166,logseq____"^Hlogseq____",142,536870922]],[logseq____"^15logseq____",[166,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[166,logseq____"^;logseq____",logseq____"~u6531e478-0821-41df-9293-8629fd309b64logseq____",536870922]],[logseq____"^15logseq____",[167,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nLlogseq____&=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big||x-3|logseq____<5\\\\right\\\\}=(-2,8)\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[167,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[167,logseq____"^Flogseq____",181,536870922]],[logseq____"^15logseq____",[167,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[167,logseq____"^Vlogseq____",170,536870922]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[167,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[167,logseq____"^;logseq____",logseq____"~u6531e478-469c-43eb-8b96-f0514af0650blogseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1}\\\\quad xlogseq____<3$\\n\\\\begin{align}\\n|x-3|logseq____&=-x+3\\\\\\\\\\n-x+3logseq____&logseq____<5 logseq____&|logseq____&-3\\\\\\\\\\n-xlogseq____&logseq____<2 logseq____&|logseq____&*-1\\\\\\\\\\nxlogseq____&logseq____>-2\\\\\\\\\\nL_1logseq____&=(-2,3)\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[168,logseq____"^Flogseq____",216,536870922]],[logseq____"^15logseq____",[168,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[168,logseq____"^Vlogseq____",216,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[168,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[168,logseq____"^;logseq____",logseq____"~u6531e478-5b57-4bfb-9cf1-5a8e90c601balogseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 3}\\\\quad xlogseq____>3$\\n\\\\begin{align}\\nx+5logseq____&logseq____>0\\\\\\\\\\n|x+5|logseq____&=x+5\\\\\\\\\\nx-3logseq____&\\\\ge0\\\\\\\\\\n|x-3|logseq____&=x-3\\\\\\\\\\nx+5logseq____&logseq____<2(x-3)\\\\\\\\\\nx+5logseq____&logseq____<2x-3 logseq____&|logseq____& -2x-5\\\\\\\\\\n-xlogseq____&logseq____<-11 logseq____&|logseq____& *(-1)\\\\\\\\\\nxlogseq____&logseq____>11\\n\\\\end{align}\\n\\\\begin{align}\\nL_3=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____>3,xlogseq____>11\\\\right\\\\}=(11,\\\\infty)\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[169,logseq____"^Flogseq____",210,536870922]],[logseq____"^15logseq____",[169,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[169,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[169,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[169,logseq____"^;logseq____",logseq____"~u6531e478-c113-474f-9830-16bc95b018f1logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[170,logseq____"^Flogseq____",191,536870922]],[logseq____"^15logseq____",[170,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[170,logseq____"^Vlogseq____",199,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[170,logseq____"^Hlogseq____",68,536870922]],[logseq____"^15logseq____",[170,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[170,logseq____"^;logseq____",logseq____"~u6531e478-2fdb-44b5-9f75-70751551b443logseq____",536870922]],[logseq____"^15logseq____",[171,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1} \\\\quad xlogseq____<-5$\\n\\\\begin{align}\\nx+5logseq____&logseq____<0\\\\\\\\\\n|x+5|logseq____&=-(x+5)=-x-5\\\\\\\\\\nx-3logseq____&logseq____<0\\\\\\\\\\n|x-3|logseq____&=-(x-3)=-x+3\\\\\\\\\\n-x-5logseq____&logseq____< 2(-x+3)\\\\\\\\\\n-x-5logseq____&logseq____<-2x+6 logseq____&|logseq____&+5+2x\\\\\\\\\\nxlogseq____<11\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____<-5,x\\\\le11\\\\right\\\\}=(-\\\\infty,-5)\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[171,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[171,logseq____"^Flogseq____",189,536870922]],[logseq____"^15logseq____",[171,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[171,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[171,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[171,logseq____"^;logseq____",logseq____"~u6531e478-d970-4b55-b64c-dcae9e6bc305logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&=x-3\\\\\\\\\\nx-3\\\\le|x+2|\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[172,logseq____"^Flogseq____",166,536870922]],[logseq____"^15logseq____",[172,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[172,logseq____"^Vlogseq____",166,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[172,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[172,logseq____"^;logseq____",logseq____"~u6531e478-6258-42f5-bfab-4f1f61b2cda4logseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Qlogseq____",logseq____"## [[Hyperbel]]logseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[173,logseq____"^Flogseq____",193,536870922]],[logseq____"^15logseq____",[173,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[173,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",151,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[173,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870922]],[logseq____"^15logseq____",[173,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[173,logseq____"^Hlogseq____",151,536870922]],[logseq____"^15logseq____",[173,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[173,logseq____"^;logseq____",logseq____"~u6531e478-ac87-427f-b9ba-bcc358e1b9d1logseq____",536870922]],[logseq____"^15logseq____",[174,logseq____"^Qlogseq____",logseq____"wie [[Ellipse]] nur statt [[Summe]] [[Differenz]]logseq____",536870922]],[logseq____"^15logseq____",[174,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[174,logseq____"^Flogseq____",173,536870922]],[logseq____"^15logseq____",[174,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[174,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",152,536870922]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",155,536870922]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[174,logseq____"^Hlogseq____",143,536870922]],[logseq____"^15logseq____",[174,logseq____"^Hlogseq____",152,536870922]],[logseq____"^15logseq____",[174,logseq____"^Hlogseq____",155,536870922]],[logseq____"^15logseq____",[174,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[174,logseq____"^;logseq____",logseq____"~u6531e478-7105-4f65-818f-5b0c0b795eb9logseq____",536870922]],[logseq____"^15logseq____",[175,logseq____"^Qlogseq____",logseq____"$\\\\{a,b,c\\\\}$logseq____",536870922]],[logseq____"^15logseq____",[175,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[175,logseq____"^Flogseq____",197,536870922]],[logseq____"^15logseq____",[175,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[175,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[175,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[175,logseq____"^;logseq____",logseq____"~u6531e478-8159-488f-9552-2a376a5e3213logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Qlogseq____",logseq____"Der [[Betrag]] ist der zu [[Abstand]] 0\\n\\\\begin{align}\\nf(x)=logseq____&|x|:=logseq____&\\\\begin{cases}\\nxlogseq____&x\\\\ge0\\\\\\\\\\n-xlogseq____&xlogseq____<0\\n\\\\end{cases}\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[176,logseq____"^Flogseq____",205,536870922]],[logseq____"^15logseq____",[176,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[176,logseq____"^Vlogseq____",205,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",150,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[176,logseq____"^Hlogseq____",150,536870922]],[logseq____"^15logseq____",[176,logseq____"^Hlogseq____",153,536870922]],[logseq____"^15logseq____",[176,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[176,logseq____"^;logseq____",logseq____"~u6531e478-c471-4a49-aa97-305021bcdb8alogseq____",536870922]],[logseq____"^15logseq____",[177,logseq____"^Qlogseq____",logseq____"[Menge]([[Mengen]]) an [Punkten]([[Punkte]]) $(x,y)$ der [Ebene]([[Ebenen]]) bei denen die [[Summe]] der [Abstände]([[Abstand]]) der Punkte zu zwei [festen Punkten]([[Fester Punkt]]) $F_1,F_2$ ([Brennpunkte]([[Brennpunkt]])) [[konstant]] istlogseq____",536870922]],[logseq____"^15logseq____",[177,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[177,logseq____"^Flogseq____",193,536870922]],[logseq____"^15logseq____",[177,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[177,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",140,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",145,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",147,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",150,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",152,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",157,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[177,logseq____"^Hlogseq____",140,536870922]],[logseq____"^15logseq____",[177,logseq____"^Hlogseq____",145,536870922]],[logseq____"^15logseq____",[177,logseq____"^Hlogseq____",147,536870922]],[logseq____"^15logseq____",[177,logseq____"^Hlogseq____",150,536870922]],[logseq____"^15logseq____",[177,logseq____"^Hlogseq____",152,536870922]],[logseq____"^15logseq____",[177,logseq____"^Hlogseq____",157,536870922]],[logseq____"^15logseq____",[177,logseq____"^Hlogseq____",158,536870922]],[logseq____"^15logseq____",[177,logseq____"^Hlogseq____",159,536870922]],[logseq____"^15logseq____",[177,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[177,logseq____"^;logseq____",logseq____"~u6531e478-8efa-4ee8-b2a5-395c8a34f4falogseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Qlogseq____",logseq____"logseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[178,logseq____"^Flogseq____",177,536870922]],[logseq____"^15logseq____",[178,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[178,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[178,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[178,logseq____"^;logseq____",logseq____"~u6531e478-fdcf-4f45-814b-f066da97fd2dlogseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Qlogseq____",logseq____"$y=\\\\frac ba x, y=-\\\\frac ba x$ sind [Asymptoten]([[Asymptote]]) der [[Hyperbel]]logseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[179,logseq____"^Flogseq____",211,536870922]],[logseq____"^15logseq____",[179,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[179,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",148,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",151,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[179,logseq____"^Hlogseq____",148,536870922]],[logseq____"^15logseq____",[179,logseq____"^Hlogseq____",151,536870922]],[logseq____"^15logseq____",[179,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[179,logseq____"^;logseq____",logseq____"~u6531e478-56fc-42e7-bede-4b5dce8e1819logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nLlogseq____&=L_1\\\\cup L_2\\\\cup L_3=\\\\left(-\\\\infty,\\\\frac13\\\\right)\\\\cup\\\\left(11,\\\\infty\\\\right)\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[180,logseq____"^Flogseq____",169,536870922]],[logseq____"^15logseq____",[180,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[180,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[180,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[180,logseq____"^;logseq____",logseq____"~u6531e478-ae26-4691-904b-aa93b8e5973clogseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Qlogseq____",logseq____"\\\\begin{gather}\\n\\\\frac{|x+5|}{|x-3|}logseq____<2\\\\quad\\\\Bigm|*|x-3|\\\\qquad x\\\\ne3\\\\\\\\\\nL=\\\\left\\\\{ x\\\\in \\\\Reals \\\\Big| |x+5|logseq____<2|x-3|\\\\right\\\\}\\\\\\\\\\n\\\\end{gather}logseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[181,logseq____"^Flogseq____",200,536870922]],[logseq____"^15logseq____",[181,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[181,logseq____"^Vlogseq____",170,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[181,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[181,logseq____"^;logseq____",logseq____"~u6531e478-c9ab-4145-8cfc-f55b6b175d4dlogseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Qlogseq____",logseq____"## [[Kreis]]logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[182,logseq____"^Flogseq____",205,536870922]],[logseq____"^15logseq____",[182,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[182,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",139,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[182,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870922]],[logseq____"^15logseq____",[182,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[182,logseq____"^Hlogseq____",139,536870922]],[logseq____"^15logseq____",[182,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[182,logseq____"^;logseq____",logseq____"~u6531e478-bf63-4e4f-b78e-801b62df4544logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Qlogseq____",logseq____"### [[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[183,logseq____"^Flogseq____",202,536870922]],[logseq____"^15logseq____",[183,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[183,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[183,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870922]],[logseq____"^15logseq____",[183,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[183,logseq____"^Hlogseq____",68,536870922]],[logseq____"^15logseq____",[183,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[183,logseq____"^;logseq____",logseq____"~u6531e478-9404-4418-a9b4-b653eab2cc19logseq____",536870922]],[logseq____"^15logseq____",[184,logseq____"^Qlogseq____",logseq____"$\\\\text{Punkt}(a,0)$\\n\\\\begin{align}\\nl_1logseq____&=a+e\\\\\\\\\\nl_2logseq____&=a-e\\\\\\\\\\nllogseq____&=2a,\\\\quad a=\\\\frac l2\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[184,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[184,logseq____"^Flogseq____",198,536870922]],[logseq____"^15logseq____",[184,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[184,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[184,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[184,logseq____"^;logseq____",logseq____"~u6531e478-7673-449f-9ff1-19231ad56fa9logseq____",536870922]],[logseq____"^15logseq____",[185,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2b}\\\\quad xlogseq____<-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____<0}logseq____&=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&\\\\le -x-2 logseq____&|logseq____&+x\\\\\\\\\\n3logseq____&\\\\le-2logseq____&logseq____&\\\\underset{falsche Aussage}{f.A}\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[185,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[185,logseq____"^Flogseq____",194,536870922]],[logseq____"^15logseq____",[185,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[185,logseq____"^Vlogseq____",166,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[185,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[185,logseq____"^;logseq____",logseq____"~u6531e478-eeb0-44da-b54e-7eb29237fa87logseq____",536870922]],[logseq____"^15logseq____",[186,logseq____"^Qlogseq____",logseq____"logseq____",536870922]],[logseq____"^15logseq____",[186,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[186,logseq____"^Flogseq____",178,536870922]],[logseq____"^15logseq____",[186,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[186,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[186,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[186,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[186,logseq____"^;logseq____",logseq____"~u6531e478-edf2-4fd2-aa65-160ed79a7f59logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\text{Ellipse}logseq____&=\\\\left\\\\{(x,y)\\\\middle|\\\\frac{x^2}{a^2}+\\\\frac{y^2}{b^2}=1\\\\right\\\\}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Flogseq____",192,536870922]],[logseq____"^15logseq____",[187,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[187,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[187,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[187,logseq____"^;logseq____",logseq____"~u6531e478-597e-4b16-bf74-4d99bf38a66clogseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nM=\\\\left\\\\{\\\\underbrace{(x,y)}_\\\\text{Punkte der Ebene}\\\\in\\\\Reals^2\\\\middle|y=|x|\\\\right\\\\}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Flogseq____",204,536870922]],[logseq____"^15logseq____",[188,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[188,logseq____"^Vlogseq____",204,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[188,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[188,logseq____"^;logseq____",logseq____"~u6531e478-b87d-4c7c-a6d5-d7d9adb7d2c9logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Qlogseq____",logseq____"### Lösung mit [[Fallunterscheidung]]logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Flogseq____",181,536870922]],[logseq____"^15logseq____",[189,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[189,logseq____"^Vlogseq____",181,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[189,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870922]],[logseq____"^15logseq____",[189,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",142,536870922]],[logseq____"^15logseq____",[189,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[189,logseq____"^;logseq____",logseq____"~u6531e478-fb88-4bfa-8c65-e6b0a159e3calogseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Qlogseq____",logseq____"[Menge]([[Mengen]]) von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]]) die den gleichen [[Abstand]] r ([[Radius]]) zu einem [festen Punkt]([[Fester Punkt]]) ([[Mittelpunkt]])logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Flogseq____",182,536870922]],[logseq____"^15logseq____",[190,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[190,logseq____"^Vlogseq____",182,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",139,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",140,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",141,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",144,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",150,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",157,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",158,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",140,536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",141,536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",144,536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",150,536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",157,536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",158,536870922]],[logseq____"^15logseq____",[190,logseq____"^Hlogseq____",159,536870922]],[logseq____"^15logseq____",[190,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[190,logseq____"^;logseq____",logseq____"~u6531e478-4479-4b16-814f-32ce3403a9f0logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Qlogseq____",logseq____"Regeln bei [[Ungleichungen]] sind Anwendbar aberlogseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Flogseq____",199,536870922]],[logseq____"^15logseq____",[191,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[191,logseq____"^Vlogseq____",199,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",146,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[191,logseq____"^Hlogseq____",146,536870922]],[logseq____"^15logseq____",[191,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[191,logseq____"^;logseq____",logseq____"~u6531e478-1ebf-4c07-b7c9-561eedd185ddlogseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Qlogseq____",logseq____"$\\\\text{Punkt(0,b)}$\\n\\\\begin{align}\\nl_1logseq____&=\\\\sqrt{b^2+e^2}=a\\\\\\\\\\nl_1^2logseq____&=b^2+e^2\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Flogseq____",184,536870922]],[logseq____"^15logseq____",[192,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[192,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[192,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[192,logseq____"^;logseq____",logseq____"~u6531e478-b305-4581-9408-bc5277302ffelogseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Qlogseq____",logseq____"## [[Ellipse]]logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Flogseq____",182,536870922]],[logseq____"^15logseq____",[193,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[193,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[193,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870922]],[logseq____"^15logseq____",[193,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[193,logseq____"^Hlogseq____",143,536870922]],[logseq____"^15logseq____",[193,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[193,logseq____"^;logseq____",logseq____"~u6531e478-2bf0-422d-907f-ecf31c8ea173logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2a}\\\\quad x\\\\ge-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{\\\\ge0}logseq____&=x+2\\\\\\\\\\n-x+3logseq____&\\\\le x+2 logseq____&|logseq____& -2\\\\\\\\\\n-x+1logseq____&\\\\le x logseq____&|logseq____& +x\\\\\\\\\\n\\\\frac12logseq____&\\\\le x logseq____&|logseq____& :2\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____<3,x\\\\ge-2,x\\\\ge\\\\frac12\\\\right\\\\}=\\\\left[\\\\frac12,3\\\\right)\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Flogseq____",160,536870922]],[logseq____"^15logseq____",[194,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[194,logseq____"^Vlogseq____",166,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[194,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[194,logseq____"^;logseq____",logseq____"~u6531e478-8bd1-4084-a201-286f2a083432logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Qlogseq____",logseq____"[[Beispiele]]\\n\\\\begin{align}\\n|5|=logseq____&5\\\\\\\\\\n|-3,3|logseq____&=3,3\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Flogseq____",176,536870922]],[logseq____"^15logseq____",[195,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[195,logseq____"^Vlogseq____",205,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[195,logseq____"^Hlogseq____",68,536870922]],[logseq____"^15logseq____",[195,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[195,logseq____"^;logseq____",logseq____"~u6531e478-7474-41e0-b61c-da287d84d541logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Qlogseq____",logseq____"logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Flogseq____",201,536870922]],[logseq____"^15logseq____",[196,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[196,logseq____"^Vlogseq____",182,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",139,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[196,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[196,logseq____"^;logseq____",logseq____"~u6531e478-4e87-48a7-a855-6ee6b0b04814logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Qlogseq____",logseq____"# [[Mengen]]logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Flogseq____",154,536870922]],[logseq____"^15logseq____",[197,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[197,logseq____"^Vlogseq____",154,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[197,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870922]],[logseq____"^15logseq____",[197,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[197,logseq____"^Hlogseq____",159,536870922]],[logseq____"^15logseq____",[197,logseq____"^17logseq____",false,536870922]],[logseq____"^15logseq____",[197,logseq____"^;logseq____",logseq____"~u6531e478-52d5-4bbd-876f-647d0221b58blogseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nelogseq____&=\\\\text{Exzentrizität}\\\\\\\\\\nl_1 + l_2 logseq____&= l\\\\\\\\\\nllogseq____&=2\\\\sqrt{a^2+e^2}\\\\\\\\\\n\\\\frac{l^2}4logseq____&=b^2+e^2\\\\\\\\\\nb^2logseq____&=\\\\frac{l^2}4-e^2\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Flogseq____",186,536870922]],[logseq____"^15logseq____",[198,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[198,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[198,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[198,logseq____"^;logseq____",logseq____"~u6531e478-e1c7-439d-80c4-7bfcc1c9594elogseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Qlogseq____",logseq____"### [[Betragsungleichungen]]logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Flogseq____",195,536870922]],[logseq____"^15logseq____",[199,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[199,logseq____"^Vlogseq____",205,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[199,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870922]],[logseq____"^15logseq____",[199,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[199,logseq____"^Hlogseq____",156,536870922]],[logseq____"^15logseq____",[199,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[199,logseq____"^;logseq____",logseq____"~u6531e478-9e03-43e6-8ada-d8889c10a23elogseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Qlogseq____",logseq____"$$L=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_{0\\\\notin L}\\\\:\\\\middle|\\\\:\\\\underbrace{|x-3|\\\\le|x+2}_{1\\\\in L}\\\\right\\\\}$$\\n$0\\\\notin L\\\\rightarrow\\\\text{0 steht nicht in Lösungsmenge}$\\n$1\\\\in L\\\\rightarrow\\\\text{1 gehört zu Lösungsmenge}$logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Flogseq____",170,536870922]],[logseq____"^15logseq____",[200,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[200,logseq____"^Vlogseq____",170,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[200,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[200,logseq____"^;logseq____",logseq____"~u6531e478-4f26-4969-a7fc-182ae1b2d278logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Qlogseq____",logseq____"$(x_M,y_M)$ haben\\n\\\\begin{align}\\n\\\\underbrace{r=\\\\sqrt{(x-x_M)^2+(y-y_M)^2}}_\\\\text{Pythagoras: Abstand zwischen 2 Punkten}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Flogseq____",190,536870922]],[logseq____"^15logseq____",[201,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[201,logseq____"^Vlogseq____",182,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",139,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[201,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[201,logseq____"^;logseq____",logseq____"~u6531e478-68bf-4b04-abc6-89af2792aaf5logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Qlogseq____",logseq____"## [[Lösungsmengen]]logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Flogseq____",175,536870922]],[logseq____"^15logseq____",[202,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[202,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",149,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[202,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870922]],[logseq____"^15logseq____",[202,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[202,logseq____"^Hlogseq____",149,536870922]],[logseq____"^15logseq____",[202,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[202,logseq____"^;logseq____",logseq____"~u6531e478-73dc-49ee-b69b-025c68d66f12logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&=-x+3\\\\\\\\\\nx-3logseq____&logseq____<5 logseq____&|logseq____&+3\\\\\\\\\\nxlogseq____&logseq____<8\\\\\\\\\\nL_2logseq____&=[3,8)\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Flogseq____",168,536870922]],[logseq____"^15logseq____",[203,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[203,logseq____"^Vlogseq____",216,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[203,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[203,logseq____"^;logseq____",logseq____"~u6531e478-f072-48bf-9586-2d67b2d392eelogseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Qlogseq____",logseq____"logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Flogseq____",214,536870922]],[logseq____"^15logseq____",[204,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[204,logseq____"^Vlogseq____",163,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[204,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[204,logseq____"^;logseq____",logseq____"~u6531e478-0ea9-48bc-8659-951649d8bbfalogseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Qlogseq____",logseq____"## [[Betrag]]logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Flogseq____",183,536870922]],[logseq____"^15logseq____",[205,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[205,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[205,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870922]],[logseq____"^15logseq____",[205,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[205,logseq____"^Hlogseq____",153,536870922]],[logseq____"^15logseq____",[205,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[205,logseq____"^;logseq____",logseq____"~u6531e478-500b-46b2-8813-bb1482732697logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1b}\\\\quad xlogseq____<-2\\\\quad\\\\text{Wiederspricht Bedingung}\\\\quad x\\\\ge3$logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Flogseq____",164,536870922]],[logseq____"^15logseq____",[206,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[206,logseq____"^Vlogseq____",166,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[206,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[206,logseq____"^;logseq____",logseq____"~u6531e478-f309-41d1-a148-891dd4c55431logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Qlogseq____",logseq____"Menge aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____<xlogseq____<4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes interval}\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Flogseq____",208,536870922]],[logseq____"^15logseq____",[207,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[207,logseq____"^Vlogseq____",183,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[207,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[207,logseq____"^;logseq____",logseq____"~u6531e478-7c8b-4c10-9c2e-4de7172df70blogseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Qlogseq____",logseq____"Menge aller reellen Zahlen zwischen 1 und 4 inklusive 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1\\\\le x\\\\le4\\\\right\\\\}=:\\\\underbrace{[-1,4]}_\\\\text{Abgeschlossenes Interval}\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Flogseq____",183,536870922]],[logseq____"^15logseq____",[208,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[208,logseq____"^Vlogseq____",183,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[208,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[208,logseq____"^;logseq____",logseq____"~u6531e478-7520-4873-b52d-399ddbe9bf30logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Qlogseq____",logseq____"a, b Halbachsen der Ellipselogseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Flogseq____",187,536870922]],[logseq____"^15logseq____",[209,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[209,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",143,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[209,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[209,logseq____"^;logseq____",logseq____"~u6531e478-e5bd-4cb3-bcf9-7b7fe8747d93logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2}\\\\quad -5\\\\le xlogseq____<3$\\n\\\\begin{align}\\nx+5logseq____&\\\\le0\\\\\\\\\\n|x+5|logseq____&=x+5\\\\\\\\\\nx-3logseq____&logseq____<0\\\\\\\\\\n|x-3|logseq____&=-(x-3)=-x+3\\\\\\\\\\nx+5logseq____&logseq____<2(-x+3)\\\\\\\\\\nx+5logseq____&logseq____<-2x+6 logseq____&|logseq____&+2x\\\\\\\\\\n3xlogseq____&logseq____<1 logseq____&|logseq____& :3\\\\\\\\\\nxlogseq____&logseq____<\\\\frac13\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-5\\\\le xlogseq____<3,xlogseq____<\\\\frac13\\\\right\\\\}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Flogseq____",171,536870922]],[logseq____"^15logseq____",[210,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[210,logseq____"^Vlogseq____",189,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[210,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[210,logseq____"^;logseq____",logseq____"~u6531e478-a654-47ad-8274-cfe3fdac3855logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\frac{x^2}{a^2}-\\\\frac{y^2}{b^2}logseq____&=1\\\\\\\\\\n\\\\text{Hyperbel}logseq____&=\\\\left\\\\{(x,y)\\\\middle|\\\\frac{x^2}{a^2}-\\\\frac{y^2}{b^2}=1\\\\right\\\\}\\\\\\\\\\ny^2logseq____&=\\\\frac{b^2}{a^2}x^2-b^2\\\\\\\\\\ny^2logseq____&=\\\\frac{b^2}{a^2}\\\\left(x^2-\\\\frac1{a^2}\\\\right)\\\\\\\\\\nylogseq____&=\\\\pm\\\\frac ba \\\\sqrt{x^2-\\\\frac1{a^2}}\\\\\\\\\\nylogseq____&=\\\\pm\\\\frac ba |x| \\\\underbrace{\\\\sqrt{1-\\\\frac1{a^2x^2}}}_{\\\\rightarrow 1}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Flogseq____",162,536870922]],[logseq____"^15logseq____",[211,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[211,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[211,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[211,logseq____"^;logseq____",logseq____"~u6531e478-6cf8-44c1-a761-b0233263f101logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup L_2=(-2,8)\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Flogseq____",203,536870922]],[logseq____"^15logseq____",[212,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[212,logseq____"^Vlogseq____",216,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[212,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[212,logseq____"^;logseq____",logseq____"~u6531e478-1341-4a05-b385-b2d2c5ab71d1logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Qlogseq____",logseq____"Menge aller rellen Zahlen zwischen 4 und $\\\\infty$ ohne 4 und $\\\\infty$\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____>4\\\\right\\\\}=:(4,\\\\infty)\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Flogseq____",207,536870922]],[logseq____"^15logseq____",[213,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[213,logseq____"^Vlogseq____",183,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[213,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[213,logseq____"^;logseq____",logseq____"~u6531e478-b2d0-4db0-a097-f81776b4d25dlogseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Qlogseq____",logseq____"logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Flogseq____",163,536870922]],[logseq____"^15logseq____",[214,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[214,logseq____"^Vlogseq____",163,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[214,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[214,logseq____"^;logseq____",logseq____"~u6531e478-8635-432e-975d-a53a146da429logseq____",536870922]],[logseq____"^15logseq____",[215,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nK=\\\\left\\\\{(x,y)\\\\in \\\\Reals^2 \\\\Big| (x-x_M)^2+(y-y_M)^2=r^2\\\\right\\\\}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[215,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[215,logseq____"^Flogseq____",196,536870922]],[logseq____"^15logseq____",[215,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[215,logseq____"^Vlogseq____",182,536870922]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",139,536870922]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[215,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[215,logseq____"^;logseq____",logseq____"~u6531e478-588e-4e07-b2bf-060b2a21f947logseq____",536870922]],[logseq____"^15logseq____",[216,logseq____"^Qlogseq____",logseq____"### Lösung mit [[Fallunterscheidung]]logseq____",536870922]],[logseq____"^15logseq____",[216,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[216,logseq____"^Flogseq____",167,536870922]],[logseq____"^15logseq____",[216,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[216,logseq____"^Vlogseq____",167,536870922]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",68,536870922]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",142,536870922]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[216,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870922]],[logseq____"^15logseq____",[216,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[216,logseq____"^Hlogseq____",142,536870922]],[logseq____"^15logseq____",[216,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[216,logseq____"^;logseq____",logseq____"~u6531e478-eb70-4442-bf05-bf1d27cbecfdlogseq____",536870922]],[logseq____"^15logseq____",[217,logseq____"^Qlogseq____",logseq____"Bei Multiplikation oder Division mit einem Betrag einer negativen Zahl nicht Anwendbar, da ein [[Betrag]] immer Positiv istlogseq____",536870922]],[logseq____"^15logseq____",[217,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[217,logseq____"^Flogseq____",191,536870922]],[logseq____"^15logseq____",[217,logseq____"^Xlogseq____",154,536870922]],[logseq____"^15logseq____",[217,logseq____"^Vlogseq____",191,536870922]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",146,536870922]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",153,536870922]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",154,536870922]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",156,536870922]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",159,536870922]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",153,536870922]],[logseq____"^15logseq____",[217,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[217,logseq____"^;logseq____",logseq____"~u6531e478-39a2-4273-ae76-1c0f76e87236logseq____",536870922]],[logseq____"^15logseq____",[219,logseq____"^Klogseq____",1697768568426,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[219,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ylogseq____",logseq____"grundlagen und diskrete strukturenlogseq____",536870923]],[logseq____"^15logseq____",[219,logseq____"^11logseq____",logseq____"Grundlagen und Diskrete Strukturenlogseq____",536870923]],[logseq____"^15logseq____",[219,logseq____"^Blogseq____",1697768568426,536870923]],[logseq____"^15logseq____",[219,logseq____"^;logseq____",logseq____"~u6531e478-d588-493b-b408-4e2c166ba3d0logseq____",536870932]],[logseq____"^15logseq____",[220,logseq____"^Klogseq____",1697768568426,536870923]],[logseq____"^15logseq____",[220,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ylogseq____",logseq____"grundlagen und diskrete strukturen/23-10-10logseq____",536870923]],[logseq____"^15logseq____",[220,logseq____"^Alogseq____",219,536870923]],[logseq____"^15logseq____",[220,logseq____"^11logseq____",logseq____"Grundlagen und Diskrete Strukturen/23-10-10logseq____",536870923]],[logseq____"^15logseq____",[220,logseq____"^Blogseq____",1697768568426,536870923]],[logseq____"^15logseq____",[220,logseq____"^;logseq____",logseq____"~u6531e478-0b94-4eb6-9e0e-db78f6749296logseq____",536870924]],[logseq____"^15logseq____",[221,logseq____"^Qlogseq____",logseq____"[[Grundlagen und Diskrete Strukturen/23-10-10]]logseq____",536870923]],[logseq____"^15logseq____",[221,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[221,logseq____"^Flogseq____",219,536870923]],[logseq____"^15logseq____",[221,logseq____"^Xlogseq____",219,536870923]],[logseq____"^15logseq____",[221,logseq____"^Vlogseq____",219,536870923]],[logseq____"^15logseq____",[221,logseq____"^Ulogseq____",219,536870923]],[logseq____"^15logseq____",[221,logseq____"^Ulogseq____",220,536870923]],[logseq____"^15logseq____",[221,logseq____"^Hlogseq____",219,536870923]],[logseq____"^15logseq____",[221,logseq____"^Hlogseq____",220,536870923]],[logseq____"^15logseq____",[221,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[221,logseq____"^;logseq____",logseq____"~u6531e478-7898-427b-b6d2-92752f5ebc39logseq____",536870923]],[logseq____"^15logseq____",[223,logseq____"^Klogseq____",1697768568546,536870924]],[logseq____"^15logseq____",[223,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[223,logseq____"^Ylogseq____",logseq____"wahrheitswerteverlauflogseq____",536870924]],[logseq____"^15logseq____",[223,logseq____"^11logseq____",logseq____"Wahrheitswerteverlauflogseq____",536870924]],[logseq____"^15logseq____",[223,logseq____"^Blogseq____",1697768568546,536870924]],[logseq____"^15logseq____",[223,logseq____"^;logseq____",logseq____"~u6531e478-721d-461c-8f99-881edc2f3d92logseq____",536870924]],[logseq____"^15logseq____",[224,logseq____"^Klogseq____",1697768568530,536870924]],[logseq____"^15logseq____",[224,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[224,logseq____"^Ylogseq____",logseq____"aussagenlogische variablelogseq____",536870924]],[logseq____"^15logseq____",[224,logseq____"^11logseq____",logseq____"Aussagenlogische Variablelogseq____",536870924]],[logseq____"^15logseq____",[224,logseq____"^Blogseq____",1697768568530,536870924]],[logseq____"^15logseq____",[224,logseq____"^;logseq____",logseq____"~u6531e478-1ff1-4a72-9424-91a073901847logseq____",536870924]],[logseq____"^15logseq____",[225,logseq____"^Klogseq____",1697768568524,536870924]],[logseq____"^15logseq____",[225,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[225,logseq____"^Ylogseq____",logseq____"wikipedialogseq____",536870924]],[logseq____"^15logseq____",[225,logseq____"^11logseq____",logseq____"Wikipedialogseq____",536870924]],[logseq____"^15logseq____",[225,logseq____"^Blogseq____",1697768568524,536870924]],[logseq____"^15logseq____",[225,logseq____"^;logseq____",logseq____"~u6531e478-09ff-43f8-bd47-6216a7d72126logseq____",536870924]],[logseq____"^15logseq____",[226,logseq____"^Klogseq____",1697768568535,536870924]],[logseq____"^15logseq____",[226,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[226,logseq____"^Ylogseq____",logseq____"formellogseq____",536870924]],[logseq____"^15logseq____",[226,logseq____"^11logseq____",logseq____"Formellogseq____",536870924]],[logseq____"^15logseq____",[226,logseq____"^Blogseq____",1697768568535,536870924]],[logseq____"^15logseq____",[226,logseq____"^;logseq____",logseq____"~u6531e478-91c3-4bba-8588-79ae4653d984logseq____",536870924]],[logseq____"^15logseq____",[227,logseq____"^Klogseq____",1697768568535,536870924]],[logseq____"^15logseq____",[227,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[227,logseq____"^Ylogseq____",logseq____"wahrheitswertlogseq____",536870924]],[logseq____"^15logseq____",[227,logseq____"^11logseq____",logseq____"Wahrheitswertlogseq____",536870924]],[logseq____"^15logseq____",[227,logseq____"^Blogseq____",1697768568535,536870924]],[logseq____"^15logseq____",[227,logseq____"^;logseq____",logseq____"~u6531e478-d1ee-4035-a7d6-f3760f9d75c0logseq____",536870925]],[logseq____"^15logseq____",[228,logseq____"^Klogseq____",1697768568523,536870924]],[logseq____"^15logseq____",[228,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[228,logseq____"^Ylogseq____",logseq____"\\logseq____"mathematische grundlagen der informatik\\logseq____", 5. auflage 2011logseq____",536870924]],[logseq____"^15logseq____",[228,logseq____"^11logseq____",logseq____"\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011logseq____",536870924]],[logseq____"^15logseq____",[228,logseq____"^Blogseq____",1697768568523,536870924]],[logseq____"^15logseq____",[228,logseq____"^;logseq____",logseq____"~u6531e478-b9bb-4727-a0a5-13134b488a39logseq____",536870924]],[logseq____"^15logseq____",[229,logseq____"^Klogseq____",1697768568547,536870924]],[logseq____"^15logseq____",[229,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[229,logseq____"^Ylogseq____",logseq____"tantologielogseq____",536870924]],[logseq____"^15logseq____",[229,logseq____"^11logseq____",logseq____"Tantologielogseq____",536870924]],[logseq____"^15logseq____",[229,logseq____"^Blogseq____",1697768568547,536870924]],[logseq____"^15logseq____",[229,logseq____"^;logseq____",logseq____"~u6531e478-ee1f-40e0-b039-e860c4cb76f7logseq____",536870924]],[logseq____"^15logseq____",[230,logseq____"^Klogseq____",1697768568544,536870924]],[logseq____"^15logseq____",[230,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[230,logseq____"^Ylogseq____",logseq____"kontradiktionlogseq____",536870924]],[logseq____"^15logseq____",[230,logseq____"^11logseq____",logseq____"Kontradiktionlogseq____",536870924]],[logseq____"^15logseq____",[230,logseq____"^Blogseq____",1697768568544,536870924]],[logseq____"^15logseq____",[230,logseq____"^;logseq____",logseq____"~u6531e478-3218-4a5f-93d6-eb57cd01d2fdlogseq____",536870924]],[logseq____"^15logseq____",[231,logseq____"^Klogseq____",1697768568533,536870924]],[logseq____"^15logseq____",[231,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[231,logseq____"^Ylogseq____",logseq____"variablenlogseq____",536870924]],[logseq____"^15logseq____",[231,logseq____"^11logseq____",logseq____"Variablenlogseq____",536870924]],[logseq____"^15logseq____",[231,logseq____"^Blogseq____",1697768568533,536870924]],[logseq____"^15logseq____",[231,logseq____"^;logseq____",logseq____"~u6531e478-f702-4f0c-84d0-be319c64f5b7logseq____",536870925]],[logseq____"^15logseq____",[232,logseq____"^Klogseq____",1697768568528,536870924]],[logseq____"^15logseq____",[232,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[232,logseq____"^Ylogseq____",logseq____"semantiklogseq____",536870924]],[logseq____"^15logseq____",[232,logseq____"^11logseq____",logseq____"Semantiklogseq____",536870924]],[logseq____"^15logseq____",[232,logseq____"^Blogseq____",1697768568528,536870924]],[logseq____"^15logseq____",[232,logseq____"^;logseq____",logseq____"~u6531e478-4ed0-4b22-b8c1-8f71fc5da5bflogseq____",536870924]],[logseq____"^15logseq____",[233,logseq____"^Klogseq____",1697768568546,536870924]],[logseq____"^15logseq____",[233,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[233,logseq____"^Ylogseq____",logseq____"logisch äquivalentlogseq____",536870924]],[logseq____"^15logseq____",[233,logseq____"^11logseq____",logseq____"Logisch Äquivalentlogseq____",536870924]],[logseq____"^15logseq____",[233,logseq____"^Blogseq____",1697768568546,536870924]],[logseq____"^15logseq____",[233,logseq____"^;logseq____",logseq____"~u6531e478-50df-4097-93d5-e27cbd4a38f0logseq____",536870924]],[logseq____"^15logseq____",[234,logseq____"^Klogseq____",1697768568534,536870924]],[logseq____"^15logseq____",[234,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[234,logseq____"^Ylogseq____",logseq____"tabellenregelnlogseq____",536870924]],[logseq____"^15logseq____",[234,logseq____"^11logseq____",logseq____"Tabellenregelnlogseq____",536870924]],[logseq____"^15logseq____",[234,logseq____"^Blogseq____",1697768568534,536870924]],[logseq____"^15logseq____",[234,logseq____"^;logseq____",logseq____"~u6531e478-8239-4d11-8a38-5e566127cb82logseq____",536870924]],[logseq____"^15logseq____",[235,logseq____"^Klogseq____",1697768568527,536870924]],[logseq____"^15logseq____",[235,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[235,logseq____"^Ylogseq____",logseq____"aussagenlogseq____",536870924]],[logseq____"^15logseq____",[235,logseq____"^11logseq____",logseq____"Aussagenlogseq____",536870924]],[logseq____"^15logseq____",[235,logseq____"^Blogseq____",1697768568527,536870924]],[logseq____"^15logseq____",[235,logseq____"^;logseq____",logseq____"~u6531e478-67f5-4a42-9bd6-c967a85b8e3blogseq____",536870925]],[logseq____"^15logseq____",[236,logseq____"^Klogseq____",1697768568532,536870924]],[logseq____"^15logseq____",[236,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[236,logseq____"^Ylogseq____",logseq____"verknüpfungenlogseq____",536870924]],[logseq____"^15logseq____",[236,logseq____"^11logseq____",logseq____"Verknüpfungenlogseq____",536870924]],[logseq____"^15logseq____",[236,logseq____"^Blogseq____",1697768568532,536870924]],[logseq____"^15logseq____",[236,logseq____"^;logseq____",logseq____"~u6531e478-f007-4073-a0fa-09fc56e86ce9logseq____",536870924]],[logseq____"^15logseq____",[237,logseq____"^Klogseq____",1697768568533,536870924]],[logseq____"^15logseq____",[237,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[237,logseq____"^Ylogseq____",logseq____"aussageformellogseq____",536870924]],[logseq____"^15logseq____",[237,logseq____"^11logseq____",logseq____"Aussageformellogseq____",536870924]],[logseq____"^15logseq____",[237,logseq____"^Blogseq____",1697768568533,536870924]],[logseq____"^15logseq____",[237,logseq____"^;logseq____",logseq____"~u6531e478-d1f5-449c-8b2b-a1952062a98elogseq____",536870924]],[logseq____"^15logseq____",[238,logseq____"^Klogseq____",1697768568529,536870924]],[logseq____"^15logseq____",[238,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[238,logseq____"^Ylogseq____",logseq____"syntaxlogseq____",536870924]],[logseq____"^15logseq____",[238,logseq____"^11logseq____",logseq____"Syntaxlogseq____",536870924]],[logseq____"^15logseq____",[238,logseq____"^Blogseq____",1697768568529,536870924]],[logseq____"^15logseq____",[238,logseq____"^;logseq____",logseq____"~u6531e478-c042-45ee-99d9-2bea98722875logseq____",536870924]],[logseq____"^15logseq____",[239,logseq____"^Klogseq____",1697768568526,536870924]],[logseq____"^15logseq____",[239,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[239,logseq____"^Ylogseq____",logseq____"verknüpfung von aussagenlogseq____",536870924]],[logseq____"^15logseq____",[239,logseq____"^11logseq____",logseq____"Verknüpfung von Aussagenlogseq____",536870924]],[logseq____"^15logseq____",[239,logseq____"^Blogseq____",1697768568526,536870924]],[logseq____"^15logseq____",[239,logseq____"^;logseq____",logseq____"~u6531e478-02a9-4612-b416-a12c594bd145logseq____",536870924]],[logseq____"^15logseq____",[240,logseq____"^Klogseq____",1697768568546,536870924]],[logseq____"^15logseq____",[240,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[240,logseq____"^Ylogseq____",logseq____"schreibweiselogseq____",536870924]],[logseq____"^15logseq____",[240,logseq____"^11logseq____",logseq____"Schreibweiselogseq____",536870924]],[logseq____"^15logseq____",[240,logseq____"^Blogseq____",1697768568546,536870924]],[logseq____"^15logseq____",[240,logseq____"^;logseq____",logseq____"~u6531e478-d8cf-4bdd-a344-2147e7c6c1fblogseq____",536870924]],[logseq____"^15logseq____",[241,logseq____"^Klogseq____",1697768568535,536870924]],[logseq____"^15logseq____",[241,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[241,logseq____"^Ylogseq____",logseq____"belegunglogseq____",536870924]],[logseq____"^15logseq____",[241,logseq____"^11logseq____",logseq____"Belegunglogseq____",536870924]],[logseq____"^15logseq____",[241,logseq____"^Blogseq____",1697768568535,536870924]],[logseq____"^15logseq____",[241,logseq____"^;logseq____",logseq____"~u6531e478-5879-4779-951d-0e22f1129870logseq____",536870924]],[logseq____"^15logseq____",[242,logseq____"^Qlogseq____",logseq____"[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____",536870924]],[logseq____"^15logseq____",[242,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[242,logseq____"^Flogseq____",267,536870924]],[logseq____"^15logseq____",[242,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[242,logseq____"^Vlogseq____",267,536870924]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",224,536870924]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",231,536870924]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[242,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[242,logseq____"^Hlogseq____",231,536870924]],[logseq____"^15logseq____",[242,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[242,logseq____"^;logseq____",logseq____"~u6531e478-5282-4953-b8a4-7f0d3c243d16logseq____",536870924]],[logseq____"^15logseq____",[243,logseq____"^Qlogseq____",logseq____"Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____",536870924]],[logseq____"^15logseq____",[243,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[243,logseq____"^Flogseq____",262,536870924]],[logseq____"^15logseq____",[243,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[243,logseq____"^Vlogseq____",262,536870924]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",227,536870924]],[logseq____"^15logseq____",[243,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[243,logseq____"^Hlogseq____",227,536870924]],[logseq____"^15logseq____",[243,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[243,logseq____"^;logseq____",logseq____"~u6531e478-bd25-46aa-8147-bba143e5c578logseq____",536870924]],[logseq____"^15logseq____",[244,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870924]],[logseq____"^15logseq____",[244,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[244,logseq____"^Flogseq____",250,536870924]],[logseq____"^15logseq____",[244,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[244,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",223,536870924]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",237,536870924]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[244,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870924]],[logseq____"^15logseq____",[244,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[244,logseq____"^Hlogseq____",223,536870924]],[logseq____"^15logseq____",[244,logseq____"^Hlogseq____",237,536870924]],[logseq____"^15logseq____",[244,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[244,logseq____"^;logseq____",logseq____"~u6531e478-152e-4173-b541-d1dbae253afdlogseq____",536870924]],[logseq____"^15logseq____",[245,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870924]],[logseq____"^15logseq____",[245,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[245,logseq____"^Flogseq____",220,536870924]],[logseq____"^15logseq____",[245,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[245,logseq____"^Vlogseq____",220,536870924]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[245,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870924]],[logseq____"^15logseq____",[245,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[245,logseq____"^17logseq____",false,536870924]],[logseq____"^15logseq____",[245,logseq____"^;logseq____",logseq____"~u6531e478-d558-4693-accc-3256ab1cc4aelogseq____",536870924]],[logseq____"^15logseq____",[246,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870924]],[logseq____"^15logseq____",[246,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[246,logseq____"^Flogseq____",268,536870924]],[logseq____"^15logseq____",[246,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[246,logseq____"^Vlogseq____",245,536870924]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",225,536870924]],[logseq____"^15logseq____",[246,logseq____"^Hlogseq____",225,536870924]],[logseq____"^15logseq____",[246,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[246,logseq____"^;logseq____",logseq____"~u6531e478-02b2-4b49-be3c-a3014112fb58logseq____",536870924]],[logseq____"^15logseq____",[247,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870924]],[logseq____"^15logseq____",[247,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[247,logseq____"^Flogseq____",244,536870924]],[logseq____"^15logseq____",[247,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[247,logseq____"^Vlogseq____",244,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",223,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",226,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",227,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",234,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",237,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",241,536870924]],[logseq____"^15logseq____",[247,logseq____"^Hlogseq____",226,536870924]],[logseq____"^15logseq____",[247,logseq____"^Hlogseq____",227,536870924]],[logseq____"^15logseq____",[247,logseq____"^Hlogseq____",234,536870924]],[logseq____"^15logseq____",[247,logseq____"^Hlogseq____",241,536870924]],[logseq____"^15logseq____",[247,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[247,logseq____"^;logseq____",logseq____"~u6531e478-b29f-438c-a374-3e2b4e1125bclogseq____",536870924]],[logseq____"^15logseq____",[248,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870924]],[logseq____"^15logseq____",[248,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[248,logseq____"^Flogseq____",258,536870924]],[logseq____"^15logseq____",[248,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[248,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",68,536870924]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[248,logseq____"^Hlogseq____",68,536870924]],[logseq____"^15logseq____",[248,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[248,logseq____"^;logseq____",logseq____"~u6531e478-9117-4b4f-b5cb-56298e0da77elogseq____",536870924]],[logseq____"^15logseq____",[249,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870924]],[logseq____"^15logseq____",[249,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[249,logseq____"^Flogseq____",264,536870924]],[logseq____"^15logseq____",[249,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[249,logseq____"^Vlogseq____",262,536870924]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[249,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870924]],[logseq____"^15logseq____",[249,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[249,logseq____"^Hlogseq____",239,536870924]],[logseq____"^15logseq____",[249,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[249,logseq____"^;logseq____",logseq____"~u6531e478-6b28-4e80-8aa4-7cf00391ea2blogseq____",536870924]],[logseq____"^15logseq____",[250,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der [[Variablen]])logseq____",536870924]],[logseq____"^15logseq____",[250,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[250,logseq____"^Flogseq____",254,536870924]],[logseq____"^15logseq____",[250,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[250,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",231,536870924]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",241,536870924]],[logseq____"^15logseq____",[250,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870924]],[logseq____"^15logseq____",[250,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[250,logseq____"^Hlogseq____",231,536870924]],[logseq____"^15logseq____",[250,logseq____"^Hlogseq____",241,536870924]],[logseq____"^15logseq____",[250,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[250,logseq____"^;logseq____",logseq____"~u6531e478-6d63-4668-ba61-575993317cb1logseq____",536870924]],[logseq____"^15logseq____",[251,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870924]],[logseq____"^15logseq____",[251,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[251,logseq____"^Flogseq____",254,536870924]],[logseq____"^15logseq____",[251,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[251,logseq____"^Vlogseq____",254,536870924]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",75,536870924]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",236,536870924]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",237,536870924]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[251,logseq____"^Hlogseq____",75,536870924]],[logseq____"^15logseq____",[251,logseq____"^Hlogseq____",236,536870924]],[logseq____"^15logseq____",[251,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[251,logseq____"^;logseq____",logseq____"~u6531e478-22a0-4b4e-800d-9c3b1d94d5b2logseq____",536870924]],[logseq____"^15logseq____",[252,logseq____"^Qlogseq____",logseq____"### [[Tantologie]]logseq____",536870924]],[logseq____"^15logseq____",[252,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[252,logseq____"^Flogseq____",244,536870924]],[logseq____"^15logseq____",[252,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[252,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",229,536870924]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[252,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870924]],[logseq____"^15logseq____",[252,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[252,logseq____"^Hlogseq____",229,536870924]],[logseq____"^15logseq____",[252,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[252,logseq____"^;logseq____",logseq____"~u6531e478-66dd-4c4d-91b5-e93b40007757logseq____",536870924]],[logseq____"^15logseq____",[253,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870924]],[logseq____"^15logseq____",[253,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[253,logseq____"^Flogseq____",252,536870924]],[logseq____"^15logseq____",[253,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[253,logseq____"^Vlogseq____",252,536870924]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",229,536870924]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[253,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[253,logseq____"^;logseq____",logseq____"~u6531e478-561a-4e02-aa7d-92ddcc83b234logseq____",536870924]],[logseq____"^15logseq____",[254,logseq____"^Qlogseq____",logseq____"### [[Aussageformel]]logseq____",536870924]],[logseq____"^15logseq____",[254,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[254,logseq____"^Flogseq____",267,536870924]],[logseq____"^15logseq____",[254,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[254,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",237,536870924]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[254,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870924]],[logseq____"^15logseq____",[254,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[254,logseq____"^Hlogseq____",237,536870924]],[logseq____"^15logseq____",[254,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[254,logseq____"^;logseq____",logseq____"~u6531e478-0d6c-4656-8919-93637890d8eelogseq____",536870924]],[logseq____"^15logseq____",[255,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____",536870924]],[logseq____"^15logseq____",[255,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[255,logseq____"^Flogseq____",248,536870924]],[logseq____"^15logseq____",[255,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[255,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",227,536870924]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",232,536870924]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",234,536870924]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",238,536870924]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[255,logseq____"^Hlogseq____",227,536870924]],[logseq____"^15logseq____",[255,logseq____"^Hlogseq____",232,536870924]],[logseq____"^15logseq____",[255,logseq____"^Hlogseq____",234,536870924]],[logseq____"^15logseq____",[255,logseq____"^Hlogseq____",238,536870924]],[logseq____"^15logseq____",[255,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[255,logseq____"^;logseq____",logseq____"~u6531e478-31d6-4609-b65f-f0e572b1a429logseq____",536870924]],[logseq____"^15logseq____",[256,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870924]],[logseq____"^15logseq____",[256,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[256,logseq____"^Flogseq____",247,536870924]],[logseq____"^15logseq____",[256,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[256,logseq____"^Vlogseq____",244,536870924]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",223,536870924]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",237,536870924]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[256,logseq____"^Hlogseq____",223,536870924]],[logseq____"^15logseq____",[256,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[256,logseq____"^;logseq____",logseq____"~u6531e478-05c2-4536-a37a-40711ca3a1cblogseq____",536870924]],[logseq____"^15logseq____",[257,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&\\\\rightarrow q logseq____&\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[257,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[257,logseq____"^Flogseq____",265,536870924]],[logseq____"^15logseq____",[257,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[257,logseq____"^Vlogseq____",265,536870924]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",68,536870924]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[257,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[257,logseq____"^;logseq____",logseq____"~u6531e478-a5d3-4009-a670-96419937b0d2logseq____",536870924]],[logseq____"^15logseq____",[258,logseq____"^Qlogseq____",logseq____"Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&\\\\quadlogseq____& (\\logseq____"\\\\text{und}\\logseq____")\\\\\\\\\\n(p\\\\lor q) logseq____&logseq____& (\\logseq____"\\\\text{oder}\\logseq____")\\\\\\\\\\n(\\\\neg p) logseq____&logseq____& (\\logseq____"\\\\text{nicht}\\logseq____")\\\\\\\\\\n(p\\\\rightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{impliziert}\\logseq____")\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{genau dann wenn}\\logseq____")\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[258,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[258,logseq____"^Flogseq____",249,536870924]],[logseq____"^15logseq____",[258,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[258,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[258,logseq____"^Hlogseq____",235,536870924]],[logseq____"^15logseq____",[258,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[258,logseq____"^;logseq____",logseq____"~u6531e478-7c15-4eb6-a1b1-f0095756e056logseq____",536870924]],[logseq____"^15logseq____",[259,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870924]],[logseq____"^15logseq____",[259,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[259,logseq____"^Flogseq____",252,536870924]],[logseq____"^15logseq____",[259,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[259,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",230,536870924]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[259,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870924]],[logseq____"^15logseq____",[259,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[259,logseq____"^Hlogseq____",230,536870924]],[logseq____"^15logseq____",[259,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[259,logseq____"^;logseq____",logseq____"~u6531e478-bbba-4157-9a8d-1e3c326dc691logseq____",536870924]],[logseq____"^15logseq____",[260,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870924]],[logseq____"^15logseq____",[260,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[260,logseq____"^Flogseq____",259,536870924]],[logseq____"^15logseq____",[260,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[260,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",223,536870924]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",233,536870924]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",240,536870924]],[logseq____"^15logseq____",[260,logseq____"^Hlogseq____",223,536870924]],[logseq____"^15logseq____",[260,logseq____"^Hlogseq____",233,536870924]],[logseq____"^15logseq____",[260,logseq____"^Hlogseq____",240,536870924]],[logseq____"^15logseq____",[260,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[260,logseq____"^;logseq____",logseq____"~u6531e478-de34-4cf6-a683-aa85049d2e8dlogseq____",536870924]],[logseq____"^15logseq____",[261,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870924]],[logseq____"^15logseq____",[261,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[261,logseq____"^Flogseq____",260,536870924]],[logseq____"^15logseq____",[261,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[261,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",229,536870924]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",229,536870924]],[logseq____"^15logseq____",[261,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[261,logseq____"^;logseq____",logseq____"~u6531e478-6a2d-4227-8a57-1a77eb86beb0logseq____",536870924]],[logseq____"^15logseq____",[262,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870924]],[logseq____"^15logseq____",[262,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[262,logseq____"^Flogseq____",245,536870924]],[logseq____"^15logseq____",[262,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[262,logseq____"^Vlogseq____",220,536870924]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[262,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870924]],[logseq____"^15logseq____",[262,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[262,logseq____"^Hlogseq____",235,536870924]],[logseq____"^15logseq____",[262,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[262,logseq____"^;logseq____",logseq____"~u6531e478-cff9-44e1-8678-19c8eeee7c3dlogseq____",536870924]],[logseq____"^15logseq____",[263,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870924]],[logseq____"^15logseq____",[263,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[263,logseq____"^Flogseq____",259,536870924]],[logseq____"^15logseq____",[263,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[263,logseq____"^Vlogseq____",259,536870924]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",230,536870924]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[263,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[263,logseq____"^;logseq____",logseq____"~u6531e478-0898-45d5-a11c-d4b9de18157elogseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&\\logseq____"5\\\\text{ ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Flogseq____",243,536870924]],[logseq____"^15logseq____",[264,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[264,logseq____"^Vlogseq____",262,536870924]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[264,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[264,logseq____"^;logseq____",logseq____"~u6531e478-a9bf-4919-94bf-e4ccb420e1b7logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Qlogseq____",logseq____"Weitere [[Beispiele]]logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Flogseq____",261,536870924]],[logseq____"^15logseq____",[265,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[265,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",68,536870924]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[265,logseq____"^Hlogseq____",68,536870924]],[logseq____"^15logseq____",[265,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[265,logseq____"^;logseq____",logseq____"~u6531e478-1fa6-4902-9cb7-577f3084b70flogseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Flogseq____",248,536870924]],[logseq____"^15logseq____",[266,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[266,logseq____"^Vlogseq____",248,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",68,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[266,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[266,logseq____"^;logseq____",logseq____"~u6531e478-bb6f-4805-b04c-3ef901379c6flogseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Qlogseq____",logseq____"### [[Aussagenlogische Variable]]logseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Flogseq____",255,536870924]],[logseq____"^15logseq____",[267,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[267,logseq____"^Vlogseq____",249,536870924]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",224,536870924]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[267,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",3],536870924]],[logseq____"^15logseq____",[267,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[267,logseq____"^Hlogseq____",224,536870924]],[logseq____"^15logseq____",[267,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[267,logseq____"^;logseq____",logseq____"~u6531e478-bd48-4dd1-bcb0-3abafb99a993logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Flogseq____",245,536870924]],[logseq____"^15logseq____",[268,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[268,logseq____"^Vlogseq____",245,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",228,536870924]],[logseq____"^15logseq____",[268,logseq____"^Hlogseq____",228,536870924]],[logseq____"^15logseq____",[268,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[268,logseq____"^;logseq____",logseq____"~u6531e478-f1b4-4cce-9503-30784a0ecbb1logseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Flogseq____",250,536870924]],[logseq____"^15logseq____",[269,logseq____"^Xlogseq____",220,536870924]],[logseq____"^15logseq____",[269,logseq____"^Vlogseq____",250,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",220,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",231,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",235,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",237,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",241,536870924]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",231,536870924]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",237,536870924]],[logseq____"^15logseq____",[269,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[269,logseq____"^;logseq____",logseq____"~u6531e478-3659-4b1b-a7bd-352e5e8e8c22logseq____",536870924]],[logseq____"^15logseq____",[271,logseq____"^Klogseq____",1697768568737,536870925]],[logseq____"^15logseq____",[271,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[271,logseq____"^Ylogseq____",logseq____"regelnlogseq____",536870925]],[logseq____"^15logseq____",[271,logseq____"^11logseq____",logseq____"Regelnlogseq____",536870925]],[logseq____"^15logseq____",[271,logseq____"^Blogseq____",1697768568737,536870925]],[logseq____"^15logseq____",[271,logseq____"^;logseq____",logseq____"~u6531e478-9ae9-4720-9878-d2c24ae1b7e1logseq____",536870925]],[logseq____"^15logseq____",[272,logseq____"^Klogseq____",1697768568722,536870925]],[logseq____"^15logseq____",[272,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[272,logseq____"^Ylogseq____",logseq____"de morgansche regelnlogseq____",536870925]],[logseq____"^15logseq____",[272,logseq____"^11logseq____",logseq____"de Morgansche Regelnlogseq____",536870925]],[logseq____"^15logseq____",[272,logseq____"^Blogseq____",1697768568722,536870925]],[logseq____"^15logseq____",[272,logseq____"^;logseq____",logseq____"~u6531e478-d9d3-41d9-ae75-a3f4e823b809logseq____",536870925]],[logseq____"^15logseq____",[273,logseq____"^Klogseq____",1697768568746,536870925]],[logseq____"^15logseq____",[273,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[273,logseq____"^Ylogseq____",logseq____"q.e.d.logseq____",536870925]],[logseq____"^15logseq____",[273,logseq____"^11logseq____",logseq____"Q.E.D.logseq____",536870925]],[logseq____"^15logseq____",[273,logseq____"^Blogseq____",1697768568746,536870925]],[logseq____"^15logseq____",[273,logseq____"^;logseq____",logseq____"~u6531e478-445a-45ff-a2e3-94a5d1f2fa08logseq____",536870933]],[logseq____"^15logseq____",[274,logseq____"^Klogseq____",1697768568738,536870925]],[logseq____"^15logseq____",[274,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[274,logseq____"^Ylogseq____",logseq____"große de morgansche regelnlogseq____",536870925]],[logseq____"^15logseq____",[274,logseq____"^11logseq____",logseq____"Große de Morgansche Regelnlogseq____",536870925]],[logseq____"^15logseq____",[274,logseq____"^Blogseq____",1697768568738,536870925]],[logseq____"^15logseq____",[274,logseq____"^;logseq____",logseq____"~u6531e478-4d4f-4685-b97d-621f80d43e2dlogseq____",536870925]],[logseq____"^15logseq____",[275,logseq____"^Klogseq____",1697768568730,536870925]],[logseq____"^15logseq____",[275,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[275,logseq____"^Ylogseq____",logseq____"aussagenlogiklogseq____",536870925]],[logseq____"^15logseq____",[275,logseq____"^11logseq____",logseq____"Aussagenlogiklogseq____",536870925]],[logseq____"^15logseq____",[275,logseq____"^Blogseq____",1697768568730,536870925]],[logseq____"^15logseq____",[275,logseq____"^;logseq____",logseq____"~u6531e478-990f-4ccb-bb24-9f1529c8fcf5logseq____",536870925]],[logseq____"^15logseq____",[276,logseq____"^Klogseq____",1697768568744,536870925]],[logseq____"^15logseq____",[276,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[276,logseq____"^Ylogseq____",logseq____"w.z.b.w.logseq____",536870925]],[logseq____"^15logseq____",[276,logseq____"^11logseq____",logseq____"w.z.b.w.logseq____",536870925]],[logseq____"^15logseq____",[276,logseq____"^Blogseq____",1697768568744,536870925]],[logseq____"^15logseq____",[276,logseq____"^;logseq____",logseq____"~u6531e478-09c7-43f4-b7ce-149952a3b739logseq____",536870933]],[logseq____"^15logseq____",[277,logseq____"^Klogseq____",1697768568725,536870925]],[logseq____"^15logseq____",[277,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[277,logseq____"^Ylogseq____",logseq____"kommutativlogseq____",536870925]],[logseq____"^15logseq____",[277,logseq____"^11logseq____",logseq____"kommutativlogseq____",536870925]],[logseq____"^15logseq____",[277,logseq____"^Blogseq____",1697768568725,536870925]],[logseq____"^15logseq____",[277,logseq____"^;logseq____",logseq____"~u6531e478-4666-4f2f-9644-5938aa5a1c84logseq____",536870925]],[logseq____"^15logseq____",[278,logseq____"^Klogseq____",1697768568742,536870925]],[logseq____"^15logseq____",[278,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[278,logseq____"^Ylogseq____",logseq____"grundlagen und diskrete strukturen/23-10-13logseq____",536870925]],[logseq____"^15logseq____",[278,logseq____"^Alogseq____",219,536870925]],[logseq____"^15logseq____",[278,logseq____"^11logseq____",logseq____"Grundlagen und Diskrete Strukturen/23-10-13logseq____",536870925]],[logseq____"^15logseq____",[278,logseq____"^Blogseq____",1697768568742,536870925]],[logseq____"^15logseq____",[278,logseq____"^;logseq____",logseq____"~u6531e478-c587-4a8c-ae9d-c79eb7613ef4logseq____",536870925]],[logseq____"^15logseq____",[279,logseq____"^Klogseq____",1697768568740,536870925]],[logseq____"^15logseq____",[279,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[279,logseq____"^Ylogseq____",logseq____"gleichartiglogseq____",536870925]],[logseq____"^15logseq____",[279,logseq____"^11logseq____",logseq____"Gleichartiglogseq____",536870925]],[logseq____"^15logseq____",[279,logseq____"^Blogseq____",1697768568740,536870925]],[logseq____"^15logseq____",[279,logseq____"^;logseq____",logseq____"~u6531e478-6feb-4f40-9d9e-e8c4bf42af63logseq____",536870925]],[logseq____"^15logseq____",[280,logseq____"^Klogseq____",1697768568723,536870925]],[logseq____"^15logseq____",[280,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[280,logseq____"^Ylogseq____",logseq____"wechselseitig distributivlogseq____",536870925]],[logseq____"^15logseq____",[280,logseq____"^11logseq____",logseq____"wechselseitig distributivlogseq____",536870925]],[logseq____"^15logseq____",[280,logseq____"^Blogseq____",1697768568723,536870925]],[logseq____"^15logseq____",[280,logseq____"^;logseq____",logseq____"~u6531e478-c410-48a5-be49-8fc21e0c8d71logseq____",536870925]],[logseq____"^15logseq____",[281,logseq____"^Klogseq____",1697768568725,536870925]],[logseq____"^15logseq____",[281,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[281,logseq____"^Ylogseq____",logseq____"assoziativlogseq____",536870925]],[logseq____"^15logseq____",[281,logseq____"^11logseq____",logseq____"assoziativlogseq____",536870925]],[logseq____"^15logseq____",[281,logseq____"^Blogseq____",1697768568725,536870925]],[logseq____"^15logseq____",[281,logseq____"^;logseq____",logseq____"~u6531e478-a9c4-48b1-b788-a2209c6ad9e2logseq____",536870925]],[logseq____"^15logseq____",[282,logseq____"^Klogseq____",1697768568746,536870925]],[logseq____"^15logseq____",[282,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[282,logseq____"^Ylogseq____",logseq____"beweiselogseq____",536870925]],[logseq____"^15logseq____",[282,logseq____"^11logseq____",logseq____"Beweiselogseq____",536870925]],[logseq____"^15logseq____",[282,logseq____"^Blogseq____",1697768568746,536870925]],[logseq____"^15logseq____",[282,logseq____"^;logseq____",logseq____"~u6531e478-8203-4583-821e-fe53fc02a292logseq____",536870925]],[logseq____"^15logseq____",[283,logseq____"^Klogseq____",1697768568741,536870925]],[logseq____"^15logseq____",[283,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[283,logseq____"^Ylogseq____",logseq____"quantorenlogseq____",536870925]],[logseq____"^15logseq____",[283,logseq____"^11logseq____",logseq____"Quantorenlogseq____",536870925]],[logseq____"^15logseq____",[283,logseq____"^Blogseq____",1697768568741,536870925]],[logseq____"^15logseq____",[283,logseq____"^;logseq____",logseq____"~u6531e478-c51e-4b4a-9dda-c2d73c2a47c4logseq____",536870925]],[logseq____"^15logseq____",[284,logseq____"^Klogseq____",1697768568736,536870925]],[logseq____"^15logseq____",[284,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[284,logseq____"^Ylogseq____",logseq____"allquantorlogseq____",536870925]],[logseq____"^15logseq____",[284,logseq____"^11logseq____",logseq____"Allquantorlogseq____",536870925]],[logseq____"^15logseq____",[284,logseq____"^Blogseq____",1697768568736,536870925]],[logseq____"^15logseq____",[284,logseq____"^;logseq____",logseq____"~u6531e478-d940-43b3-bec4-712c104b35dclogseq____",536870925]],[logseq____"^15logseq____",[285,logseq____"^Klogseq____",1697768568741,536870925]],[logseq____"^15logseq____",[285,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[285,logseq____"^Ylogseq____",logseq____"permutationlogseq____",536870925]],[logseq____"^15logseq____",[285,logseq____"^11logseq____",logseq____"Permutationlogseq____",536870925]],[logseq____"^15logseq____",[285,logseq____"^Blogseq____",1697768568741,536870925]],[logseq____"^15logseq____",[285,logseq____"^;logseq____",logseq____"~u6531e478-a767-4830-aae0-f33269221a9flogseq____",536870925]],[logseq____"^15logseq____",[286,logseq____"^Klogseq____",1697768568739,536870925]],[logseq____"^15logseq____",[286,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[286,logseq____"^Ylogseq____",logseq____"große azzoziativgesetzelogseq____",536870925]],[logseq____"^15logseq____",[286,logseq____"^11logseq____",logseq____"Große Azzoziativgesetzelogseq____",536870925]],[logseq____"^15logseq____",[286,logseq____"^Blogseq____",1697768568739,536870925]],[logseq____"^15logseq____",[286,logseq____"^;logseq____",logseq____"~u6531e478-6686-4b34-bea9-48efaab7534flogseq____",536870925]],[logseq____"^15logseq____",[287,logseq____"^Klogseq____",1697768568724,536870925]],[logseq____"^15logseq____",[287,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[287,logseq____"^Ylogseq____",logseq____"idenpotentlogseq____",536870925]],[logseq____"^15logseq____",[287,logseq____"^11logseq____",logseq____"idenpotentlogseq____",536870925]],[logseq____"^15logseq____",[287,logseq____"^Blogseq____",1697768568724,536870925]],[logseq____"^15logseq____",[287,logseq____"^;logseq____",logseq____"~u6531e478-4c88-4961-a90c-19cb539f117dlogseq____",536870925]],[logseq____"^15logseq____",[288,logseq____"^Klogseq____",1697768568723,536870925]],[logseq____"^15logseq____",[288,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[288,logseq____"^Ylogseq____",logseq____"distributivlogseq____",536870925]],[logseq____"^15logseq____",[288,logseq____"^11logseq____",logseq____"distributivlogseq____",536870925]],[logseq____"^15logseq____",[288,logseq____"^Blogseq____",1697768568723,536870925]],[logseq____"^15logseq____",[288,logseq____"^;logseq____",logseq____"~u6531e478-2b7e-4ead-8db4-439db6a255ddlogseq____",536870925]],[logseq____"^15logseq____",[289,logseq____"^Klogseq____",1697768568727,536870925]],[logseq____"^15logseq____",[289,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[289,logseq____"^Ylogseq____",logseq____"aussageformlogseq____",536870925]],[logseq____"^15logseq____",[289,logseq____"^11logseq____",logseq____"Aussageformlogseq____",536870925]],[logseq____"^15logseq____",[289,logseq____"^Blogseq____",1697768568727,536870925]],[logseq____"^15logseq____",[289,logseq____"^;logseq____",logseq____"~u6531e478-58c5-456d-b907-b85b22284e3clogseq____",536870925]],[logseq____"^15logseq____",[290,logseq____"^Klogseq____",1697768568731,536870925]],[logseq____"^15logseq____",[290,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[290,logseq____"^Ylogseq____",logseq____"existenzquantorlogseq____",536870925]],[logseq____"^15logseq____",[290,logseq____"^11logseq____",logseq____"Existenzquantorlogseq____",536870925]],[logseq____"^15logseq____",[290,logseq____"^Blogseq____",1697768568731,536870925]],[logseq____"^15logseq____",[290,logseq____"^;logseq____",logseq____"~u6531e478-6d83-4219-9504-1165edeb0ad9logseq____",536870925]],[logseq____"^15logseq____",[291,logseq____"^Klogseq____",1697768568737,536870925]],[logseq____"^15logseq____",[291,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[291,logseq____"^Ylogseq____",logseq____"negationsregelnlogseq____",536870925]],[logseq____"^15logseq____",[291,logseq____"^11logseq____",logseq____"Negationsregelnlogseq____",536870925]],[logseq____"^15logseq____",[291,logseq____"^Blogseq____",1697768568737,536870925]],[logseq____"^15logseq____",[291,logseq____"^;logseq____",logseq____"~u6531e478-f815-46f9-83bd-367edc7af704logseq____",536870925]],[logseq____"^15logseq____",[292,logseq____"^Klogseq____",1697768568728,536870925]],[logseq____"^15logseq____",[292,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[292,logseq____"^Ylogseq____",logseq____"satzlogseq____",536870925]],[logseq____"^15logseq____",[292,logseq____"^11logseq____",logseq____"Satzlogseq____",536870925]],[logseq____"^15logseq____",[292,logseq____"^Blogseq____",1697768568728,536870925]],[logseq____"^15logseq____",[292,logseq____"^;logseq____",logseq____"~u6531e478-e491-4148-b763-ff65da860adclogseq____",536870925]],[logseq____"^15logseq____",[293,logseq____"^Klogseq____",1697768568727,536870925]],[logseq____"^15logseq____",[293,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[293,logseq____"^Ylogseq____",logseq____"universen (logik)logseq____",536870925]],[logseq____"^15logseq____",[293,logseq____"^11logseq____",logseq____"Universen (Logik)logseq____",536870925]],[logseq____"^15logseq____",[293,logseq____"^Blogseq____",1697768568727,536870925]],[logseq____"^15logseq____",[293,logseq____"^;logseq____",logseq____"~u6531e478-b9d1-45e9-9727-ba07536c6f51logseq____",536870925]],[logseq____"^15logseq____",[294,logseq____"^Klogseq____",1697768568730,536870925]],[logseq____"^15logseq____",[294,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[294,logseq____"^Ylogseq____",logseq____"sprachenlogseq____",536870925]],[logseq____"^15logseq____",[294,logseq____"^11logseq____",logseq____"Sprachenlogseq____",536870925]],[logseq____"^15logseq____",[294,logseq____"^Blogseq____",1697768568730,536870925]],[logseq____"^15logseq____",[294,logseq____"^;logseq____",logseq____"~u6531e478-c6fb-4ebe-aab0-874a74809cfdlogseq____",536870925]],[logseq____"^15logseq____",[295,logseq____"^Klogseq____",1697768568728,536870925]],[logseq____"^15logseq____",[295,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[295,logseq____"^Ylogseq____",logseq____"objekt (logik)logseq____",536870925]],[logseq____"^15logseq____",[295,logseq____"^11logseq____",logseq____"Objekt (Logik)logseq____",536870925]],[logseq____"^15logseq____",[295,logseq____"^Blogseq____",1697768568728,536870925]],[logseq____"^15logseq____",[295,logseq____"^;logseq____",logseq____"~u6531e478-18a6-4b2b-abd2-319b2f393101logseq____",536870925]],[logseq____"^15logseq____",[296,logseq____"^Qlogseq____",logseq____"[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____",536870925]],[logseq____"^15logseq____",[296,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[296,logseq____"^Flogseq____",297,536870925]],[logseq____"^15logseq____",[296,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[296,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[296,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[296,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[296,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[296,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[296,logseq____"^Hlogseq____",279,536870925]],[logseq____"^15logseq____",[296,logseq____"^Hlogseq____",283,536870925]],[logseq____"^15logseq____",[296,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[296,logseq____"^;logseq____",logseq____"~u6531e478-e424-4284-917f-a7aacc7956cdlogseq____",536870925]],[logseq____"^15logseq____",[297,logseq____"^Qlogseq____",logseq____"## [[Regeln]]logseq____",536870925]],[logseq____"^15logseq____",[297,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[297,logseq____"^Flogseq____",302,536870925]],[logseq____"^15logseq____",[297,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[297,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[297,logseq____"^Ulogseq____",271,536870925]],[logseq____"^15logseq____",[297,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[297,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[297,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870925]],[logseq____"^15logseq____",[297,logseq____"^Jlogseq____",[],536870925]],[logseq____"^15logseq____",[297,logseq____"^Hlogseq____",271,536870925]],[logseq____"^15logseq____",[297,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[297,logseq____"^;logseq____",logseq____"~u6531e478-2730-4df9-9f5c-d44cdae53b6elogseq____",536870925]],[logseq____"^15logseq____",[298,logseq____"^Qlogseq____",logseq____"Nach Ersetzung von $x$ in der AF $\\logseq____"xlogseq____<y\\logseq____"$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____"17logseq____<y\\logseq____"$logseq____",536870925]],[logseq____"^15logseq____",[298,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[298,logseq____"^Flogseq____",299,536870925]],[logseq____"^15logseq____",[298,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[298,logseq____"^Vlogseq____",299,536870925]],[logseq____"^15logseq____",[298,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[298,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[298,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[298,logseq____"^;logseq____",logseq____"~u6531e478-b23e-4974-ae35-e945c856639clogseq____",536870925]],[logseq____"^15logseq____",[299,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\logseq____"\\\\text{x ist prim}\\logseq____" \\\\quad logseq____& \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____"\\\\underbrace{x}_{x_1}logseq____<\\\\underbrace{y}_{x_2}\\logseq____"\\\\quad logseq____&\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____"\\\\text{x ist wahr}\\logseq____"\\\\quadlogseq____&\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____",536870925]],[logseq____"^15logseq____",[299,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[299,logseq____"^Flogseq____",301,536870925]],[logseq____"^15logseq____",[299,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[299,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[299,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[299,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[299,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[299,logseq____"^;logseq____",logseq____"~u6531e478-3086-4f0d-ac88-c9b22e92cccclogseq____",536870925]],[logseq____"^15logseq____",[300,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870925]],[logseq____"^15logseq____",[300,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[300,logseq____"^Flogseq____",307,536870925]],[logseq____"^15logseq____",[300,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[300,logseq____"^Vlogseq____",307,536870925]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",282,536870925]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[300,logseq____"^Hlogseq____",282,536870925]],[logseq____"^15logseq____",[300,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[300,logseq____"^;logseq____",logseq____"~u6531e478-9634-4eb2-9773-7eb65a2a00aflogseq____",536870925]],[logseq____"^15logseq____",[301,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870925]],[logseq____"^15logseq____",[301,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[301,logseq____"^Flogseq____",305,536870925]],[logseq____"^15logseq____",[301,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[301,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[301,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[301,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[301,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[301,logseq____"^Hlogseq____",68,536870925]],[logseq____"^15logseq____",[301,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[301,logseq____"^;logseq____",logseq____"~u6531e478-dc3e-403f-9db9-e7395f3aed96logseq____",536870925]],[logseq____"^15logseq____",[302,logseq____"^Qlogseq____",logseq____"Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____",536870925]],[logseq____"^15logseq____",[302,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[302,logseq____"^Flogseq____",309,536870925]],[logseq____"^15logseq____",[302,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[302,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[302,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[302,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[302,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[302,logseq____"^;logseq____",logseq____"~u6531e478-714a-4448-8cf7-557c5b009ee0logseq____",536870925]],[logseq____"^15logseq____",[303,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870925]],[logseq____"^15logseq____",[303,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[303,logseq____"^Flogseq____",300,536870925]],[logseq____"^15logseq____",[303,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[303,logseq____"^Vlogseq____",307,536870925]],[logseq____"^15logseq____",[303,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[303,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[303,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[303,logseq____"^Ulogseq____",282,536870925]],[logseq____"^15logseq____",[303,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[303,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[303,logseq____"^Hlogseq____",282,536870925]],[logseq____"^15logseq____",[303,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[303,logseq____"^;logseq____",logseq____"~u6531e478-4885-4e7c-95e3-58f46ccd88f1logseq____",536870925]],[logseq____"^15logseq____",[304,logseq____"^Qlogseq____",logseq____"# [[Regeln]]logseq____",536870925]],[logseq____"^15logseq____",[304,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[304,logseq____"^Flogseq____",278,536870925]],[logseq____"^15logseq____",[304,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[304,logseq____"^Vlogseq____",278,536870925]],[logseq____"^15logseq____",[304,logseq____"^Ulogseq____",271,536870925]],[logseq____"^15logseq____",[304,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[304,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870925]],[logseq____"^15logseq____",[304,logseq____"^Jlogseq____",[],536870925]],[logseq____"^15logseq____",[304,logseq____"^Hlogseq____",271,536870925]],[logseq____"^15logseq____",[304,logseq____"^17logseq____",false,536870925]],[logseq____"^15logseq____",[304,logseq____"^;logseq____",logseq____"~u6531e478-4346-40af-b3ae-22332b8c2a6clogseq____",536870925]],[logseq____"^15logseq____",[305,logseq____"^Qlogseq____",logseq____"[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____",536870925]],[logseq____"^15logseq____",[305,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[305,logseq____"^Flogseq____",316,536870925]],[logseq____"^15logseq____",[305,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[305,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[305,logseq____"^Ulogseq____",231,536870925]],[logseq____"^15logseq____",[305,logseq____"^Ulogseq____",235,536870925]],[logseq____"^15logseq____",[305,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[305,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[305,logseq____"^Ulogseq____",292,536870925]],[logseq____"^15logseq____",[305,logseq____"^Ulogseq____",295,536870925]],[logseq____"^15logseq____",[305,logseq____"^Hlogseq____",231,536870925]],[logseq____"^15logseq____",[305,logseq____"^Hlogseq____",235,536870925]],[logseq____"^15logseq____",[305,logseq____"^Hlogseq____",292,536870925]],[logseq____"^15logseq____",[305,logseq____"^Hlogseq____",295,536870925]],[logseq____"^15logseq____",[305,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[305,logseq____"^;logseq____",logseq____"~u6531e478-ef55-4902-81e2-f11db9522d3flogseq____",536870925]],[logseq____"^15logseq____",[306,logseq____"^Qlogseq____",logseq____"Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____",536870925]],[logseq____"^15logseq____",[306,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[306,logseq____"^Flogseq____",318,536870925]],[logseq____"^15logseq____",[306,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[306,logseq____"^Vlogseq____",297,536870925]],[logseq____"^15logseq____",[306,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[306,logseq____"^Ulogseq____",271,536870925]],[logseq____"^15logseq____",[306,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[306,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[306,logseq____"^Hlogseq____",68,536870925]],[logseq____"^15logseq____",[306,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[306,logseq____"^;logseq____",logseq____"~u6531e478-cad4-4299-8dbc-e45b275910cdlogseq____",536870925]],[logseq____"^15logseq____",[307,logseq____"^Qlogseq____",logseq____"Betrachte $\\logseq____"xlogseq____<y\\logseq____"$ als AF über $\\\\Reals, \\\\Reals$logseq____",536870925]],[logseq____"^15logseq____",[307,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[307,logseq____"^Flogseq____",325,536870925]],[logseq____"^15logseq____",[307,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[307,logseq____"^Vlogseq____",325,536870925]],[logseq____"^15logseq____",[307,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[307,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[307,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[307,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[307,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[307,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[307,logseq____"^;logseq____",logseq____"~u6531e478-5bcf-472d-b92a-f8186a532ce9logseq____",536870925]],[logseq____"^15logseq____",[308,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____",536870925]],[logseq____"^15logseq____",[308,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[308,logseq____"^Flogseq____",311,536870925]],[logseq____"^15logseq____",[308,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[308,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[308,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[308,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[308,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[308,logseq____"^;logseq____",logseq____"~u6531e478-cfb0-4411-b692-cf6432282a8clogseq____",536870925]],[logseq____"^15logseq____",[309,logseq____"^Qlogseq____",logseq____"$\\\\exists x:p(x)$ ist die Aussage: \\logseq____"Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____",536870925]],[logseq____"^15logseq____",[309,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[309,logseq____"^Flogseq____",308,536870925]],[logseq____"^15logseq____",[309,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[309,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[309,logseq____"^Ulogseq____",227,536870925]],[logseq____"^15logseq____",[309,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[309,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[309,logseq____"^Hlogseq____",227,536870925]],[logseq____"^15logseq____",[309,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[309,logseq____"^;logseq____",logseq____"~u6531e478-71d1-4a16-af29-fa03fe4078b7logseq____",536870925]],[logseq____"^15logseq____",[310,logseq____"^Qlogseq____",logseq____"see: [[Allquantor]] [[Existenzquantor]]logseq____",536870925]],[logseq____"^15logseq____",[310,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[310,logseq____"^Flogseq____",308,536870925]],[logseq____"^15logseq____",[310,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[310,logseq____"^Vlogseq____",308,536870925]],[logseq____"^15logseq____",[310,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[310,logseq____"^Ulogseq____",284,536870925]],[logseq____"^15logseq____",[310,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[310,logseq____"^Ulogseq____",290,536870925]],[logseq____"^15logseq____",[310,logseq____"^Hlogseq____",284,536870925]],[logseq____"^15logseq____",[310,logseq____"^Hlogseq____",290,536870925]],[logseq____"^15logseq____",[310,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[310,logseq____"^;logseq____",logseq____"~u6531e478-df0a-430b-ba2f-f867618b9388logseq____",536870925]],[logseq____"^15logseq____",[311,logseq____"^Qlogseq____",logseq____"Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____",536870925]],[logseq____"^15logseq____",[311,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[311,logseq____"^Flogseq____",327,536870925]],[logseq____"^15logseq____",[311,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[311,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[311,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[311,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[311,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[311,logseq____"^;logseq____",logseq____"~u6531e478-2d40-4e69-8126-80c935c739c1logseq____",536870925]],[logseq____"^15logseq____",[312,logseq____"^Qlogseq____",logseq____"Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____",536870925]],[logseq____"^15logseq____",[312,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[312,logseq____"^Flogseq____",322,536870925]],[logseq____"^15logseq____",[312,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[312,logseq____"^Vlogseq____",331,536870925]],[logseq____"^15logseq____",[312,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[312,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[312,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[312,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[312,logseq____"^Hlogseq____",283,536870925]],[logseq____"^15logseq____",[312,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[312,logseq____"^;logseq____",logseq____"~u6531e478-e5e8-4c5a-b9a2-024e58ff6c97logseq____",536870925]],[logseq____"^15logseq____",[313,logseq____"^Qlogseq____",logseq____"Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____",536870925]],[logseq____"^15logseq____",[313,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[313,logseq____"^Flogseq____",299,536870925]],[logseq____"^15logseq____",[313,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[313,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[313,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[313,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[313,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[313,logseq____"^;logseq____",logseq____"~u6531e478-e65a-4bf6-9578-4b0034664876logseq____",536870925]],[logseq____"^15logseq____",[314,logseq____"^Qlogseq____",logseq____"see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____",536870925]],[logseq____"^15logseq____",[314,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[314,logseq____"^Flogseq____",329,536870925]],[logseq____"^15logseq____",[314,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[314,logseq____"^Vlogseq____",329,536870925]],[logseq____"^15logseq____",[314,logseq____"^Ulogseq____",272,536870925]],[logseq____"^15logseq____",[314,logseq____"^Ulogseq____",277,536870925]],[logseq____"^15logseq____",[314,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[314,logseq____"^Ulogseq____",280,536870925]],[logseq____"^15logseq____",[314,logseq____"^Ulogseq____",281,536870925]],[logseq____"^15logseq____",[314,logseq____"^Ulogseq____",287,536870925]],[logseq____"^15logseq____",[314,logseq____"^Ulogseq____",288,536870925]],[logseq____"^15logseq____",[314,logseq____"^Hlogseq____",272,536870925]],[logseq____"^15logseq____",[314,logseq____"^Hlogseq____",277,536870925]],[logseq____"^15logseq____",[314,logseq____"^Hlogseq____",280,536870925]],[logseq____"^15logseq____",[314,logseq____"^Hlogseq____",281,536870925]],[logseq____"^15logseq____",[314,logseq____"^Hlogseq____",287,536870925]],[logseq____"^15logseq____",[314,logseq____"^Hlogseq____",288,536870925]],[logseq____"^15logseq____",[314,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[314,logseq____"^;logseq____",logseq____"~u6531e478-b9ac-4437-a012-7c6b1268f66clogseq____",536870925]],[logseq____"^15logseq____",[315,logseq____"^Qlogseq____",logseq____"Widerspruch = ↯, #logseq____",536870925]],[logseq____"^15logseq____",[315,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[315,logseq____"^Flogseq____",321,536870925]],[logseq____"^15logseq____",[315,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[315,logseq____"^Vlogseq____",321,536870925]],[logseq____"^15logseq____",[315,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[315,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[315,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[315,logseq____"^Ulogseq____",282,536870925]],[logseq____"^15logseq____",[315,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[315,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[315,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[315,logseq____"^;logseq____",logseq____"~u6531e478-dd00-4cc9-beef-e39cd99688e6logseq____",536870925]],[logseq____"^15logseq____",[316,logseq____"^Qlogseq____",logseq____"[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____",536870925]],[logseq____"^15logseq____",[316,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[316,logseq____"^Flogseq____",319,536870925]],[logseq____"^15logseq____",[316,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[316,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[316,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[316,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[316,logseq____"^Ulogseq____",293,536870925]],[logseq____"^15logseq____",[316,logseq____"^Hlogseq____",289,536870925]],[logseq____"^15logseq____",[316,logseq____"^Hlogseq____",293,536870925]],[logseq____"^15logseq____",[316,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[316,logseq____"^;logseq____",logseq____"~u6531e478-00ad-4d40-9dbb-635e84630f5clogseq____",536870925]],[logseq____"^15logseq____",[317,logseq____"^Qlogseq____",logseq____"$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, logseq____",536870925]],[logseq____"^15logseq____",[317,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[317,logseq____"^Flogseq____",323,536870925]],[logseq____"^15logseq____",[317,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[317,logseq____"^Vlogseq____",323,536870925]],[logseq____"^15logseq____",[317,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[317,logseq____"^Ulogseq____",273,536870925]],[logseq____"^15logseq____",[317,logseq____"^Ulogseq____",276,536870925]],[logseq____"^15logseq____",[317,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[317,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[317,logseq____"^Ulogseq____",282,536870925]],[logseq____"^15logseq____",[317,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[317,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[317,logseq____"^Hlogseq____",273,536870925]],[logseq____"^15logseq____",[317,logseq____"^Hlogseq____",276,536870925]],[logseq____"^15logseq____",[317,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[317,logseq____"^;logseq____",logseq____"~u6531e478-56e4-4b5c-94b0-52ee4df75a57logseq____",536870925]],[logseq____"^15logseq____",[318,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____",536870925]],[logseq____"^15logseq____",[318,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[318,logseq____"^Flogseq____",297,536870925]],[logseq____"^15logseq____",[318,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[318,logseq____"^Vlogseq____",297,536870925]],[logseq____"^15logseq____",[318,logseq____"^Ulogseq____",271,536870925]],[logseq____"^15logseq____",[318,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[318,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[318,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[318,logseq____"^;logseq____",logseq____"~u6531e478-c95c-46f5-8254-62c967373928logseq____",536870925]],[logseq____"^15logseq____",[319,logseq____"^Qlogseq____",logseq____"# [[Aussageform]]logseq____",536870925]],[logseq____"^15logseq____",[319,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[319,logseq____"^Flogseq____",329,536870925]],[logseq____"^15logseq____",[319,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[319,logseq____"^Vlogseq____",278,536870925]],[logseq____"^15logseq____",[319,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[319,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[319,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870925]],[logseq____"^15logseq____",[319,logseq____"^Jlogseq____",[],536870925]],[logseq____"^15logseq____",[319,logseq____"^Hlogseq____",289,536870925]],[logseq____"^15logseq____",[319,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[319,logseq____"^;logseq____",logseq____"~u6531e478-9d36-40a3-b7af-317563d9f711logseq____",536870925]],[logseq____"^15logseq____",[320,logseq____"^Qlogseq____",logseq____"#FIXMElogseq____",536870925]],[logseq____"^15logseq____",[320,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[320,logseq____"^Flogseq____",302,536870925]],[logseq____"^15logseq____",[320,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[320,logseq____"^Vlogseq____",302,536870925]],[logseq____"^15logseq____",[320,logseq____"^Ulogseq____",75,536870925]],[logseq____"^15logseq____",[320,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[320,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[320,logseq____"^Hlogseq____",75,536870925]],[logseq____"^15logseq____",[320,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[320,logseq____"^;logseq____",logseq____"~u6531e478-3678-466f-88b0-26cf3cf73e26logseq____",536870925]],[logseq____"^15logseq____",[321,logseq____"^Qlogseq____",logseq____"Wäre $y$ aus $\\\\Reals$ mit $xlogseq____<y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____<y$, Widerspruch. $\\\\blacksquare$logseq____",536870925]],[logseq____"^15logseq____",[321,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[321,logseq____"^Flogseq____",303,536870925]],[logseq____"^15logseq____",[321,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[321,logseq____"^Vlogseq____",303,536870925]],[logseq____"^15logseq____",[321,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[321,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[321,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[321,logseq____"^Ulogseq____",282,536870925]],[logseq____"^15logseq____",[321,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[321,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[321,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[321,logseq____"^;logseq____",logseq____"~u6531e478-c349-45e7-825c-38d5cbce2c14logseq____",536870925]],[logseq____"^15logseq____",[322,logseq____"^Qlogseq____",logseq____"wobei $\\\\pi$ eine \\logseq____"[[Permutation]]\\logseq____" der Zahl $(1,2,\\\\cdots,n)$ istlogseq____",536870925]],[logseq____"^15logseq____",[322,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[322,logseq____"^Flogseq____",331,536870925]],[logseq____"^15logseq____",[322,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[322,logseq____"^Vlogseq____",331,536870925]],[logseq____"^15logseq____",[322,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[322,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[322,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[322,logseq____"^Ulogseq____",285,536870925]],[logseq____"^15logseq____",[322,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[322,logseq____"^Hlogseq____",285,536870925]],[logseq____"^15logseq____",[322,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[322,logseq____"^;logseq____",logseq____"~u6531e478-ce63-4403-8b40-3114b631d0e3logseq____",536870925]],[logseq____"^15logseq____",[323,logseq____"^Qlogseq____",logseq____"Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____<x+1=y$ also $xlogseq____<y$. $\\\\blacksquare$logseq____",536870925]],[logseq____"^15logseq____",[323,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[323,logseq____"^Flogseq____",300,536870925]],[logseq____"^15logseq____",[323,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[323,logseq____"^Vlogseq____",300,536870925]],[logseq____"^15logseq____",[323,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[323,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[323,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[323,logseq____"^Ulogseq____",282,536870925]],[logseq____"^15logseq____",[323,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[323,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[323,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[323,logseq____"^;logseq____",logseq____"~u6531e478-abfb-4df5-bbdb-fdaf0d252815logseq____",536870925]],[logseq____"^15logseq____",[324,logseq____"^Qlogseq____",logseq____"see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____",536870925]],[logseq____"^15logseq____",[324,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[324,logseq____"^Flogseq____",318,536870925]],[logseq____"^15logseq____",[324,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[324,logseq____"^Vlogseq____",318,536870925]],[logseq____"^15logseq____",[324,logseq____"^Ulogseq____",271,536870925]],[logseq____"^15logseq____",[324,logseq____"^Ulogseq____",274,536870925]],[logseq____"^15logseq____",[324,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[324,logseq____"^Ulogseq____",286,536870925]],[logseq____"^15logseq____",[324,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[324,logseq____"^Ulogseq____",291,536870925]],[logseq____"^15logseq____",[324,logseq____"^Hlogseq____",274,536870925]],[logseq____"^15logseq____",[324,logseq____"^Hlogseq____",286,536870925]],[logseq____"^15logseq____",[324,logseq____"^Hlogseq____",291,536870925]],[logseq____"^15logseq____",[324,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[324,logseq____"^;logseq____",logseq____"~u6531e478-a52f-417d-a9af-a8ffe33f46a5logseq____",536870925]],[logseq____"^15logseq____",[325,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870925]],[logseq____"^15logseq____",[325,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[325,logseq____"^Flogseq____",331,536870925]],[logseq____"^15logseq____",[325,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[325,logseq____"^Vlogseq____",296,536870925]],[logseq____"^15logseq____",[325,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[325,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[325,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[325,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[325,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[325,logseq____"^Hlogseq____",68,536870925]],[logseq____"^15logseq____",[325,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[325,logseq____"^;logseq____",logseq____"~u6531e478-6484-4608-b1a2-450ead187333logseq____",536870925]],[logseq____"^15logseq____",[326,logseq____"^Qlogseq____",logseq____"Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____",536870925]],[logseq____"^15logseq____",[326,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[326,logseq____"^Flogseq____",313,536870925]],[logseq____"^15logseq____",[326,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[326,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[326,logseq____"^Ulogseq____",275,536870925]],[logseq____"^15logseq____",[326,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[326,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[326,logseq____"^Ulogseq____",294,536870925]],[logseq____"^15logseq____",[326,logseq____"^Hlogseq____",275,536870925]],[logseq____"^15logseq____",[326,logseq____"^Hlogseq____",294,536870925]],[logseq____"^15logseq____",[326,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[326,logseq____"^;logseq____",logseq____"~u6531e478-a90d-483c-8097-1e36f13c71b3logseq____",536870925]],[logseq____"^15logseq____",[327,logseq____"^Qlogseq____",logseq____"Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____",536870925]],[logseq____"^15logseq____",[327,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[327,logseq____"^Flogseq____",326,536870925]],[logseq____"^15logseq____",[327,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[327,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[327,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[327,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[327,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[327,logseq____"^;logseq____",logseq____"~u6531e478-216e-48a1-b6af-7de21b128259logseq____",536870925]],[logseq____"^15logseq____",[328,logseq____"^Qlogseq____",logseq____"$\\\\forall x:p(x)$ ist die [Aussage]([[Aussagen]]): $\\logseq____"\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____"\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____",536870925]],[logseq____"^15logseq____",[328,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[328,logseq____"^Flogseq____",313,536870925]],[logseq____"^15logseq____",[328,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[328,logseq____"^Vlogseq____",313,536870925]],[logseq____"^15logseq____",[328,logseq____"^Ulogseq____",227,536870925]],[logseq____"^15logseq____",[328,logseq____"^Ulogseq____",235,536870925]],[logseq____"^15logseq____",[328,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[328,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[328,logseq____"^Hlogseq____",227,536870925]],[logseq____"^15logseq____",[328,logseq____"^Hlogseq____",235,536870925]],[logseq____"^15logseq____",[328,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[328,logseq____"^;logseq____",logseq____"~u6531e478-0cdd-4e41-9bf1-063d70c28d08logseq____",536870925]],[logseq____"^15logseq____",[329,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&\\\\equiv p, \\\\quad \\\\neg logseq____&\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____",536870925]],[logseq____"^15logseq____",[329,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[329,logseq____"^Flogseq____",304,536870925]],[logseq____"^15logseq____",[329,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[329,logseq____"^Vlogseq____",278,536870925]],[logseq____"^15logseq____",[329,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[329,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[329,logseq____"^;logseq____",logseq____"~u6531e478-e7eb-4f42-bedd-1b0806685f38logseq____",536870925]],[logseq____"^15logseq____",[330,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____",536870925]],[logseq____"^15logseq____",[330,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[330,logseq____"^Flogseq____",333,536870925]],[logseq____"^15logseq____",[330,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[330,logseq____"^Vlogseq____",333,536870925]],[logseq____"^15logseq____",[330,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[330,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[330,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[330,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[330,logseq____"^;logseq____",logseq____"~u6531e478-efd5-4c84-8233-13fa8410798blogseq____",536870925]],[logseq____"^15logseq____",[331,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____",536870925]],[logseq____"^15logseq____",[331,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[331,logseq____"^Flogseq____",296,536870925]],[logseq____"^15logseq____",[331,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[331,logseq____"^Vlogseq____",296,536870925]],[logseq____"^15logseq____",[331,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[331,logseq____"^Ulogseq____",279,536870925]],[logseq____"^15logseq____",[331,logseq____"^Ulogseq____",283,536870925]],[logseq____"^15logseq____",[331,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[331,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[331,logseq____"^;logseq____",logseq____"~u6531e478-d24a-49e5-8e0e-f4a1b2f4384clogseq____",536870925]],[logseq____"^15logseq____",[332,logseq____"^Qlogseq____",logseq____"Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____",536870925]],[logseq____"^15logseq____",[332,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[332,logseq____"^Flogseq____",306,536870925]],[logseq____"^15logseq____",[332,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[332,logseq____"^Vlogseq____",306,536870925]],[logseq____"^15logseq____",[332,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[332,logseq____"^Ulogseq____",271,536870925]],[logseq____"^15logseq____",[332,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[332,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[332,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[332,logseq____"^;logseq____",logseq____"~u6531e478-c9f0-4b35-8651-dafe6ae48e30logseq____",536870925]],[logseq____"^15logseq____",[333,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870925]],[logseq____"^15logseq____",[333,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[333,logseq____"^Flogseq____",296,536870925]],[logseq____"^15logseq____",[333,logseq____"^Xlogseq____",278,536870925]],[logseq____"^15logseq____",[333,logseq____"^Vlogseq____",319,536870925]],[logseq____"^15logseq____",[333,logseq____"^Ulogseq____",68,536870925]],[logseq____"^15logseq____",[333,logseq____"^Ulogseq____",278,536870925]],[logseq____"^15logseq____",[333,logseq____"^Ulogseq____",289,536870925]],[logseq____"^15logseq____",[333,logseq____"^Hlogseq____",68,536870925]],[logseq____"^15logseq____",[333,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[333,logseq____"^;logseq____",logseq____"~u6531e478-66ce-460a-a5a3-87bd18ae53c6logseq____",536870925]],[logseq____"^15logseq____",[335,logseq____"^Klogseq____",1697768568804,536870926]],[logseq____"^15logseq____",[335,logseq____"^@logseq____",false,536870926]],[logseq____"^15logseq____",[335,logseq____"^Ylogseq____",logseq____"logarithmusgesetzelogseq____",536870926]],[logseq____"^15logseq____",[335,logseq____"^11logseq____",logseq____"Logarithmusgesetzelogseq____",536870926]],[logseq____"^15logseq____",[335,logseq____"^Blogseq____",1697768568804,536870926]],[logseq____"^15logseq____",[335,logseq____"^;logseq____",logseq____"~u6531e478-d6b9-458e-87ff-514a45995a8clogseq____",536870926]],[logseq____"^15logseq____",[336,logseq____"^Qlogseq____",logseq____"[[Logarithmusgesetze]]logseq____",536870926]],[logseq____"^15logseq____",[336,logseq____"^Ologseq____",logseq____"^16logseq____",536870926]],[logseq____"^15logseq____",[336,logseq____"^Flogseq____",64,536870926]],[logseq____"^15logseq____",[336,logseq____"^Xlogseq____",64,536870926]],[logseq____"^15logseq____",[336,logseq____"^Vlogseq____",64,536870926]],[logseq____"^15logseq____",[336,logseq____"^Ulogseq____",64,536870926]],[logseq____"^15logseq____",[336,logseq____"^Ulogseq____",335,536870926]],[logseq____"^15logseq____",[336,logseq____"^Hlogseq____",335,536870926]],[logseq____"^15logseq____",[336,logseq____"^17logseq____",true,536870926]],[logseq____"^15logseq____",[336,logseq____"^;logseq____",logseq____"~u6531e478-d8eb-47de-afe2-5f54f945fc3dlogseq____",536870926]],[logseq____"^15logseq____",[337,logseq____"^Qlogseq____",logseq____"logseq____",536870926]],[logseq____"^15logseq____",[337,logseq____"^Ologseq____",logseq____"^16logseq____",536870926]],[logseq____"^15logseq____",[337,logseq____"^Flogseq____",336,536870926]],[logseq____"^15logseq____",[337,logseq____"^Xlogseq____",64,536870926]],[logseq____"^15logseq____",[337,logseq____"^Vlogseq____",64,536870926]],[logseq____"^15logseq____",[337,logseq____"^Ulogseq____",64,536870926]],[logseq____"^15logseq____",[337,logseq____"^17logseq____",true,536870926]],[logseq____"^15logseq____",[337,logseq____"^;logseq____",logseq____"~u6531e478-7151-4f22-acd5-1b78c2274619logseq____",536870926]],[logseq____"^15logseq____",[350,logseq____"^Klogseq____",1697768568836,536870929]],[logseq____"^15logseq____",[350,logseq____"^@logseq____",false,536870929]],[logseq____"^15logseq____",[350,logseq____"^Ylogseq____",logseq____"programmierung und algorithmenlogseq____",536870929]],[logseq____"^15logseq____",[350,logseq____"^11logseq____",logseq____"Programmierung und Algorithmenlogseq____",536870929]],[logseq____"^15logseq____",[350,logseq____"^Blogseq____",1697768568836,536870929]],[logseq____"^15logseq____",[350,logseq____"^;logseq____",logseq____"~u6531e478-eb4d-4f65-9d26-15bd6753e004logseq____",536870932]],[logseq____"^15logseq____",[351,logseq____"^Qlogseq____",logseq____"# Informationenlogseq____",536870929]],[logseq____"^15logseq____",[351,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[351,logseq____"^Flogseq____",350,536870929]],[logseq____"^15logseq____",[351,logseq____"^Xlogseq____",350,536870929]],[logseq____"^15logseq____",[351,logseq____"^Vlogseq____",350,536870929]],[logseq____"^15logseq____",[351,logseq____"^Ulogseq____",350,536870929]],[logseq____"^15logseq____",[351,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870929]],[logseq____"^15logseq____",[351,logseq____"^Jlogseq____",[],536870929]],[logseq____"^15logseq____",[351,logseq____"^17logseq____",false,536870929]],[logseq____"^15logseq____",[351,logseq____"^;logseq____",logseq____"~u6531e478-7b1b-42e5-9e41-91a2bb72f940logseq____",536870929]],[logseq____"^15logseq____",[352,logseq____"^Qlogseq____",logseq____"Bestehquote: 40%logseq____",536870929]],[logseq____"^15logseq____",[352,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[352,logseq____"^Flogseq____",351,536870929]],[logseq____"^15logseq____",[352,logseq____"^Xlogseq____",350,536870929]],[logseq____"^15logseq____",[352,logseq____"^Vlogseq____",351,536870929]],[logseq____"^15logseq____",[352,logseq____"^Ulogseq____",350,536870929]],[logseq____"^15logseq____",[352,logseq____"^17logseq____",true,536870929]],[logseq____"^15logseq____",[352,logseq____"^;logseq____",logseq____"~u6531e478-a0b7-4371-b05d-0af3c2851a79logseq____",536870929]],[logseq____"^15logseq____",[353,logseq____"^Qlogseq____",logseq____"## Bonuspunktelogseq____",536870929]],[logseq____"^15logseq____",[353,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[353,logseq____"^Flogseq____",352,536870929]],[logseq____"^15logseq____",[353,logseq____"^Xlogseq____",350,536870929]],[logseq____"^15logseq____",[353,logseq____"^Vlogseq____",351,536870929]],[logseq____"^15logseq____",[353,logseq____"^Ulogseq____",350,536870929]],[logseq____"^15logseq____",[353,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",2],536870929]],[logseq____"^15logseq____",[353,logseq____"^Jlogseq____",[],536870929]],[logseq____"^15logseq____",[353,logseq____"^17logseq____",true,536870929]],[logseq____"^15logseq____",[353,logseq____"^;logseq____",logseq____"~u6531e478-a2bc-4a0e-a5b9-e9d69a6cd0d1logseq____",536870929]],[logseq____"^15logseq____",[354,logseq____"^Qlogseq____",logseq____"Übungsblätter abgebenlogseq____",536870929]],[logseq____"^15logseq____",[354,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[354,logseq____"^Flogseq____",353,536870929]],[logseq____"^15logseq____",[354,logseq____"^Xlogseq____",350,536870929]],[logseq____"^15logseq____",[354,logseq____"^Vlogseq____",353,536870929]],[logseq____"^15logseq____",[354,logseq____"^Ulogseq____",350,536870929]],[logseq____"^15logseq____",[354,logseq____"^17logseq____",true,536870929]],[logseq____"^15logseq____",[354,logseq____"^;logseq____",logseq____"~u6531e478-c753-49e9-a4b4-6d0bbe0677felogseq____",536870929]],[logseq____"^15logseq____",[355,logseq____"^Qlogseq____",logseq____"Übungsprüfungenlogseq____",536870929]],[logseq____"^15logseq____",[355,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[355,logseq____"^Flogseq____",354,536870929]],[logseq____"^15logseq____",[355,logseq____"^Xlogseq____",350,536870929]],[logseq____"^15logseq____",[355,logseq____"^Vlogseq____",353,536870929]],[logseq____"^15logseq____",[355,logseq____"^Ulogseq____",350,536870929]],[logseq____"^15logseq____",[355,logseq____"^17logseq____",true,536870929]],[logseq____"^15logseq____",[355,logseq____"^;logseq____",logseq____"~u6531e478-5524-4afd-bb1e-172e6d712da4logseq____",536870929]],[logseq____"^15logseq____",[357,logseq____"^Qlogseq____",logseq____"# Bedeutunglogseq____",536870930]],[logseq____"^15logseq____",[357,logseq____"^Ologseq____",logseq____"^16logseq____",536870930]],[logseq____"^15logseq____",[357,logseq____"^Flogseq____",273,536870930]],[logseq____"^15logseq____",[357,logseq____"^Xlogseq____",273,536870930]],[logseq____"^15logseq____",[357,logseq____"^Vlogseq____",273,536870930]],[logseq____"^15logseq____",[357,logseq____"^Ulogseq____",273,536870930]],[logseq____"^15logseq____",[357,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870930]],[logseq____"^15logseq____",[357,logseq____"^Jlogseq____",[],536870930]],[logseq____"^15logseq____",[357,logseq____"^17logseq____",false,536870930]],[logseq____"^15logseq____",[357,logseq____"^;logseq____",logseq____"~u6531e478-5514-425e-ae18-93f964319fa0logseq____",536870930]],[logseq____"^15logseq____",[358,logseq____"^Qlogseq____",logseq____"Q.E.D. = \\logseq____"quod erat demonstrandum\\logseq____"logseq____",536870930]],[logseq____"^15logseq____",[358,logseq____"^Ologseq____",logseq____"^16logseq____",536870930]],[logseq____"^15logseq____",[358,logseq____"^Flogseq____",357,536870930]],[logseq____"^15logseq____",[358,logseq____"^Xlogseq____",273,536870930]],[logseq____"^15logseq____",[358,logseq____"^Vlogseq____",357,536870930]],[logseq____"^15logseq____",[358,logseq____"^Ulogseq____",273,536870930]],[logseq____"^15logseq____",[358,logseq____"^17logseq____",true,536870930]],[logseq____"^15logseq____",[358,logseq____"^;logseq____",logseq____"~u6531e478-2a82-4e32-bfd5-77bb0ab80a2clogseq____",536870930]],[logseq____"^15logseq____",[359,logseq____"^Qlogseq____",logseq____"lat. für \\logseq____"was zu beweisen wahr\\logseq____" (siehe [[w.z.b.w.]])logseq____",536870930]],[logseq____"^15logseq____",[359,logseq____"^Ologseq____",logseq____"^16logseq____",536870930]],[logseq____"^15logseq____",[359,logseq____"^Flogseq____",358,536870930]],[logseq____"^15logseq____",[359,logseq____"^Xlogseq____",273,536870930]],[logseq____"^15logseq____",[359,logseq____"^Vlogseq____",357,536870930]],[logseq____"^15logseq____",[359,logseq____"^Ulogseq____",273,536870930]],[logseq____"^15logseq____",[359,logseq____"^Ulogseq____",276,536870930]],[logseq____"^15logseq____",[359,logseq____"^Hlogseq____",276,536870930]],[logseq____"^15logseq____",[359,logseq____"^17logseq____",true,536870930]],[logseq____"^15logseq____",[359,logseq____"^;logseq____",logseq____"~u6531e478-3780-44dc-80c3-aa92a6ef3211logseq____",536870930]],[logseq____"^15logseq____",[360,logseq____"^Qlogseq____",logseq____"Signalisiert das Ende eines Beweiseslogseq____",536870930]],[logseq____"^15logseq____",[360,logseq____"^Ologseq____",logseq____"^16logseq____",536870930]],[logseq____"^15logseq____",[360,logseq____"^Flogseq____",359,536870930]],[logseq____"^15logseq____",[360,logseq____"^Xlogseq____",273,536870930]],[logseq____"^15logseq____",[360,logseq____"^Vlogseq____",357,536870930]],[logseq____"^15logseq____",[360,logseq____"^Ulogseq____",273,536870930]],[logseq____"^15logseq____",[360,logseq____"^17logseq____",true,536870930]],[logseq____"^15logseq____",[360,logseq____"^;logseq____",logseq____"~u6531e478-0595-4eb0-875b-96745d436243logseq____",536870930]],[logseq____"^15logseq____",[362,logseq____"^Klogseq____",1697768568861,536870931]],[logseq____"^15logseq____",[362,logseq____"^@logseq____",false,536870931]],[logseq____"^15logseq____",[362,logseq____"^Ylogseq____",logseq____"ungleichheitszeichenlogseq____",536870931]],[logseq____"^15logseq____",[362,logseq____"^11logseq____",logseq____"Ungleichheitszeichenlogseq____",536870931]],[logseq____"^15logseq____",[362,logseq____"^Blogseq____",1697768568861,536870931]],[logseq____"^15logseq____",[362,logseq____"^;logseq____",logseq____"~u6531e478-9ceb-4f8b-bba5-68ead58cecddlogseq____",536870931]],[logseq____"^15logseq____",[363,logseq____"^Klogseq____",1697768568861,536870931]],[logseq____"^15logseq____",[363,logseq____"^@logseq____",false,536870931]],[logseq____"^15logseq____",[363,logseq____"^Ylogseq____",logseq____"divisionlogseq____",536870931]],[logseq____"^15logseq____",[363,logseq____"^11logseq____",logseq____"Divisionlogseq____",536870931]],[logseq____"^15logseq____",[363,logseq____"^Blogseq____",1697768568861,536870931]],[logseq____"^15logseq____",[363,logseq____"^;logseq____",logseq____"~u6531e478-af9b-46ea-8b2f-9359a0d43f30logseq____",536870931]],[logseq____"^15logseq____",[364,logseq____"^Klogseq____",1697768568862,536870931]],[logseq____"^15logseq____",[364,logseq____"^@logseq____",false,536870931]],[logseq____"^15logseq____",[364,logseq____"^Ylogseq____",logseq____"multiplikationlogseq____",536870931]],[logseq____"^15logseq____",[364,logseq____"^11logseq____",logseq____"Multiplikationlogseq____",536870931]],[logseq____"^15logseq____",[364,logseq____"^Blogseq____",1697768568862,536870931]],[logseq____"^15logseq____",[364,logseq____"^;logseq____",logseq____"~u6531e478-c55f-4d32-9e4f-05233523f3c1logseq____",536870931]],[logseq____"^15logseq____",[365,logseq____"^Qlogseq____",logseq____"# Regelnlogseq____",536870931]],[logseq____"^15logseq____",[365,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[365,logseq____"^Flogseq____",146,536870931]],[logseq____"^15logseq____",[365,logseq____"^Xlogseq____",146,536870931]],[logseq____"^15logseq____",[365,logseq____"^Vlogseq____",146,536870931]],[logseq____"^15logseq____",[365,logseq____"^Ulogseq____",146,536870931]],[logseq____"^15logseq____",[365,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870931]],[logseq____"^15logseq____",[365,logseq____"^Jlogseq____",[],536870931]],[logseq____"^15logseq____",[365,logseq____"^17logseq____",false,536870931]],[logseq____"^15logseq____",[365,logseq____"^;logseq____",logseq____"~u6531e478-8cf5-4a57-a191-8448cd465993logseq____",536870931]],[logseq____"^15logseq____",[366,logseq____"^Qlogseq____",logseq____"Bei [[Multiplikation]] oder [[Division]] mit einer negativen Zahl wird das [[Ungleichheitszeichen]] umgekehrtlogseq____",536870931]],[logseq____"^15logseq____",[366,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[366,logseq____"^Flogseq____",365,536870931]],[logseq____"^15logseq____",[366,logseq____"^Xlogseq____",146,536870931]],[logseq____"^15logseq____",[366,logseq____"^Vlogseq____",365,536870931]],[logseq____"^15logseq____",[366,logseq____"^Ulogseq____",146,536870931]],[logseq____"^15logseq____",[366,logseq____"^Ulogseq____",362,536870931]],[logseq____"^15logseq____",[366,logseq____"^Ulogseq____",363,536870931]],[logseq____"^15logseq____",[366,logseq____"^Ulogseq____",364,536870931]],[logseq____"^15logseq____",[366,logseq____"^Hlogseq____",362,536870931]],[logseq____"^15logseq____",[366,logseq____"^Hlogseq____",363,536870931]],[logseq____"^15logseq____",[366,logseq____"^Hlogseq____",364,536870931]],[logseq____"^15logseq____",[366,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[366,logseq____"^;logseq____",logseq____"~u6531e478-9700-4363-a8f1-8e5b62c73938logseq____",536870931]],[logseq____"^15logseq____",[367,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\logseq____"logseq____>\\logseq____"logseq____&\\\\rightarrow\\logseq____"logseq____<\\logseq____"\\\\\\\\\\n\\logseq____"logseq____<\\logseq____"logseq____&\\\\rightarrow\\logseq____"logseq____>\\logseq____"\\\\\\\\\\n\\logseq____"\\\\ge\\logseq____"logseq____&\\\\rightarrow\\logseq____"\\\\le\\logseq____"\\\\\\\\\\n\\logseq____"\\\\le\\logseq____"logseq____&\\\\rightarrow\\logseq____"\\\\ge\\logseq____"\\\\\\\\\\n\\\\end{align}logseq____",536870931]],[logseq____"^15logseq____",[367,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[367,logseq____"^Flogseq____",366,536870931]],[logseq____"^15logseq____",[367,logseq____"^Xlogseq____",146,536870931]],[logseq____"^15logseq____",[367,logseq____"^Vlogseq____",366,536870931]],[logseq____"^15logseq____",[367,logseq____"^Ulogseq____",146,536870931]],[logseq____"^15logseq____",[367,logseq____"^Ulogseq____",362,536870931]],[logseq____"^15logseq____",[367,logseq____"^Ulogseq____",363,536870931]],[logseq____"^15logseq____",[367,logseq____"^Ulogseq____",364,536870931]],[logseq____"^15logseq____",[367,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[367,logseq____"^;logseq____",logseq____"~u6531e478-7879-4710-8b6f-63023193f4d5logseq____",536870931]],[logseq____"^15logseq____",[368,logseq____"^Qlogseq____",logseq____"logseq____",536870931]],[logseq____"^15logseq____",[368,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[368,logseq____"^Flogseq____",367,536870931]],[logseq____"^15logseq____",[368,logseq____"^Xlogseq____",146,536870931]],[logseq____"^15logseq____",[368,logseq____"^Vlogseq____",366,536870931]],[logseq____"^15logseq____",[368,logseq____"^Ulogseq____",146,536870931]],[logseq____"^15logseq____",[368,logseq____"^Ulogseq____",362,536870931]],[logseq____"^15logseq____",[368,logseq____"^Ulogseq____",363,536870931]],[logseq____"^15logseq____",[368,logseq____"^Ulogseq____",364,536870931]],[logseq____"^15logseq____",[368,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[368,logseq____"^;logseq____",logseq____"~u6531e478-6814-4390-808b-b63b27bc2e5dlogseq____",536870931]],[logseq____"^15logseq____",[370,logseq____"^Klogseq____",1697768568875,536870932]],[logseq____"^15logseq____",[370,logseq____"^@logseq____",false,536870932]],[logseq____"^15logseq____",[370,logseq____"^Ylogseq____",logseq____"vorlesungs notizenlogseq____",536870932]],[logseq____"^15logseq____",[370,logseq____"^11logseq____",logseq____"Vorlesungs Notizenlogseq____",536870932]],[logseq____"^15logseq____",[370,logseq____"^Blogseq____",1697768568875,536870932]],[logseq____"^15logseq____",[370,logseq____"^;logseq____",logseq____"~u6531e478-dc45-4a75-a701-29ce7d8b7563logseq____",536870932]],[logseq____"^15logseq____",[371,logseq____"^Qlogseq____",logseq____"[[Auffrischung Mathematik]]logseq____",536870932]],[logseq____"^15logseq____",[371,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[371,logseq____"^Flogseq____",370,536870932]],[logseq____"^15logseq____",[371,logseq____"^Xlogseq____",370,536870932]],[logseq____"^15logseq____",[371,logseq____"^Vlogseq____",370,536870932]],[logseq____"^15logseq____",[371,logseq____"^Ulogseq____",56,536870932]],[logseq____"^15logseq____",[371,logseq____"^Ulogseq____",370,536870932]],[logseq____"^15logseq____",[371,logseq____"^Hlogseq____",56,536870932]],[logseq____"^15logseq____",[371,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[371,logseq____"^;logseq____",logseq____"~u6531e478-38ad-4cc0-96ac-910a354a6073logseq____",536870932]],[logseq____"^15logseq____",[372,logseq____"^Qlogseq____",logseq____"[[Mathematik für Informatiker 1]]logseq____",536870932]],[logseq____"^15logseq____",[372,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[372,logseq____"^Flogseq____",371,536870932]],[logseq____"^15logseq____",[372,logseq____"^Xlogseq____",370,536870932]],[logseq____"^15logseq____",[372,logseq____"^Vlogseq____",370,536870932]],[logseq____"^15logseq____",[372,logseq____"^Ulogseq____",339,536870932]],[logseq____"^15logseq____",[372,logseq____"^Ulogseq____",370,536870932]],[logseq____"^15logseq____",[372,logseq____"^Hlogseq____",339,536870932]],[logseq____"^15logseq____",[372,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[372,logseq____"^;logseq____",logseq____"~u6531e478-1a8c-4920-af0d-9650904ffd80logseq____",536870932]],[logseq____"^15logseq____",[373,logseq____"^Qlogseq____",logseq____"[[Grundlagen und Diskrete Strukturen]]logseq____",536870932]],[logseq____"^15logseq____",[373,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[373,logseq____"^Flogseq____",372,536870932]],[logseq____"^15logseq____",[373,logseq____"^Xlogseq____",370,536870932]],[logseq____"^15logseq____",[373,logseq____"^Vlogseq____",370,536870932]],[logseq____"^15logseq____",[373,logseq____"^Ulogseq____",219,536870932]],[logseq____"^15logseq____",[373,logseq____"^Ulogseq____",370,536870932]],[logseq____"^15logseq____",[373,logseq____"^Hlogseq____",219,536870932]],[logseq____"^15logseq____",[373,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[373,logseq____"^;logseq____",logseq____"~u6531e478-512c-41f2-a130-359e1181e87dlogseq____",536870932]],[logseq____"^15logseq____",[374,logseq____"^Qlogseq____",logseq____"[[Programmierung und Algorithmen]]logseq____",536870932]],[logseq____"^15logseq____",[374,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[374,logseq____"^Flogseq____",373,536870932]],[logseq____"^15logseq____",[374,logseq____"^Xlogseq____",370,536870932]],[logseq____"^15logseq____",[374,logseq____"^Vlogseq____",370,536870932]],[logseq____"^15logseq____",[374,logseq____"^Ulogseq____",350,536870932]],[logseq____"^15logseq____",[374,logseq____"^Ulogseq____",370,536870932]],[logseq____"^15logseq____",[374,logseq____"^Hlogseq____",350,536870932]],[logseq____"^15logseq____",[374,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[374,logseq____"^;logseq____",logseq____"~u6531e478-cee8-47f5-83a8-c5014a18701elogseq____",536870932]],[logseq____"^15logseq____",[375,logseq____"^Qlogseq____",logseq____"logseq____<iframe src=\\logseq____"https://cal.lu-dev.de\\logseq____" style=\\logseq____"width: 100%; height: 1220px\\logseq____"logseq____>logseq____</iframelogseq____>logseq____",536870932]],[logseq____"^15logseq____",[375,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[375,logseq____"^Flogseq____",374,536870932]],[logseq____"^15logseq____",[375,logseq____"^Xlogseq____",370,536870932]],[logseq____"^15logseq____",[375,logseq____"^Vlogseq____",370,536870932]],[logseq____"^15logseq____",[375,logseq____"^Ulogseq____",370,536870932]],[logseq____"^15logseq____",[375,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[375,logseq____"^;logseq____",logseq____"~u6531e478-ad65-46da-9905-6912a2cdd963logseq____",536870932]],[logseq____"^15logseq____",[376,logseq____"^Qlogseq____",logseq____"logseq____",536870932]],[logseq____"^15logseq____",[376,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[376,logseq____"^Flogseq____",375,536870932]],[logseq____"^15logseq____",[376,logseq____"^Xlogseq____",370,536870932]],[logseq____"^15logseq____",[376,logseq____"^Vlogseq____",370,536870932]],[logseq____"^15logseq____",[376,logseq____"^Ulogseq____",370,536870932]],[logseq____"^15logseq____",[376,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[376,logseq____"^;logseq____",logseq____"~u6531e478-c9fa-4858-b344-ba61a000da60logseq____",536870932]],[logseq____"^15logseq____",[378,logseq____"^Qlogseq____",logseq____"# Bedeutunglogseq____",536870933]],[logseq____"^15logseq____",[378,logseq____"^Ologseq____",logseq____"^16logseq____",536870933]],[logseq____"^15logseq____",[378,logseq____"^Flogseq____",276,536870933]],[logseq____"^15logseq____",[378,logseq____"^Xlogseq____",276,536870933]],[logseq____"^15logseq____",[378,logseq____"^Vlogseq____",276,536870933]],[logseq____"^15logseq____",[378,logseq____"^Ulogseq____",276,536870933]],[logseq____"^15logseq____",[378,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^1Qlogseq____",1],536870933]],[logseq____"^15logseq____",[378,logseq____"^Jlogseq____",[],536870933]],[logseq____"^15logseq____",[378,logseq____"^17logseq____",false,536870933]],[logseq____"^15logseq____",[378,logseq____"^;logseq____",logseq____"~u6531e478-2209-4b6b-b49d-742a602947d5logseq____",536870933]],[logseq____"^15logseq____",[379,logseq____"^Qlogseq____",logseq____"w.z.b.w. = \\logseq____"was zu beweisen war\\logseq____"logseq____",536870933]],[logseq____"^15logseq____",[379,logseq____"^Ologseq____",logseq____"^16logseq____",536870933]],[logseq____"^15logseq____",[379,logseq____"^Flogseq____",378,536870933]],[logseq____"^15logseq____",[379,logseq____"^Xlogseq____",276,536870933]],[logseq____"^15logseq____",[379,logseq____"^Vlogseq____",378,536870933]],[logseq____"^15logseq____",[379,logseq____"^Ulogseq____",276,536870933]],[logseq____"^15logseq____",[379,logseq____"^17logseq____",true,536870933]],[logseq____"^15logseq____",[379,logseq____"^;logseq____",logseq____"~u6531e478-a716-4520-ab8c-01abe944a83elogseq____",536870933]],[logseq____"^15logseq____",[380,logseq____"^Qlogseq____",logseq____"Signalisiert das Ende eines Beweiseslogseq____",536870933]],[logseq____"^15logseq____",[380,logseq____"^Ologseq____",logseq____"^16logseq____",536870933]],[logseq____"^15logseq____",[380,logseq____"^Flogseq____",379,536870933]],[logseq____"^15logseq____",[380,logseq____"^Xlogseq____",276,536870933]],[logseq____"^15logseq____",[380,logseq____"^Vlogseq____",378,536870933]],[logseq____"^15logseq____",[380,logseq____"^Ulogseq____",276,536870933]],[logseq____"^15logseq____",[380,logseq____"^17logseq____",true,536870933]],[logseq____"^15logseq____",[380,logseq____"^;logseq____",logseq____"~u6531e478-8006-4988-a890-903da0081f36logseq____",536870933]],[logseq____"^15logseq____",[381,logseq____"^Qlogseq____",logseq____"siehe [[Q.E.D.]]logseq____",536870933]],[logseq____"^15logseq____",[381,logseq____"^Ologseq____",logseq____"^16logseq____",536870933]],[logseq____"^15logseq____",[381,logseq____"^Flogseq____",380,536870933]],[logseq____"^15logseq____",[381,logseq____"^Xlogseq____",276,536870933]],[logseq____"^15logseq____",[381,logseq____"^Vlogseq____",378,536870933]],[logseq____"^15logseq____",[381,logseq____"^Ulogseq____",273,536870933]],[logseq____"^15logseq____",[381,logseq____"^Ulogseq____",276,536870933]],[logseq____"^15logseq____",[381,logseq____"^Hlogseq____",273,536870933]],[logseq____"^15logseq____",[381,logseq____"^17logseq____",true,536870933]],[logseq____"^15logseq____",[381,logseq____"^;logseq____",logseq____"~u6531e478-1bc7-434d-a173-c95ab227cb0blogseq____",536870933]],[logseq____"^15logseq____",[383,logseq____"^Klogseq____",1697768568899,536870934]],[logseq____"^15logseq____",[383,logseq____"^@logseq____",false,536870934]],[logseq____"^15logseq____",[383,logseq____"^Ylogseq____",logseq____"readmelogseq____",536870934]],[logseq____"^15logseq____",[383,logseq____"^11logseq____",logseq____"READMElogseq____",536870934]],[logseq____"^15logseq____",[383,logseq____"^Blogseq____",1697768568899,536870934]],[logseq____"^15logseq____",[383,logseq____"^;logseq____",logseq____"~u6531e478-002e-4fa1-a162-93ed99866273logseq____",536870934]],[logseq____"^15logseq____",[384,logseq____"^Qlogseq____",logseq____"Branch for autogenerated assets that are accessed through through raw.githubusercontents.com\\nlogseq____",536870934]],[logseq____"^15logseq____",[384,logseq____"^Ologseq____",logseq____"^16logseq____",536870934]],[logseq____"^15logseq____",[384,logseq____"^Flogseq____",383,536870934]],[logseq____"^15logseq____",[384,logseq____"^Xlogseq____",383,536870934]],[logseq____"^15logseq____",[384,logseq____"^Vlogseq____",383,536870934]],[logseq____"^15logseq____",[384,logseq____"^Ulogseq____",383,536870934]],[logseq____"^15logseq____",[384,logseq____"^:logseq____",true,536870934]],[logseq____"^15logseq____",[384,logseq____"^Jlogseq____",[],536870934]],[logseq____"^15logseq____",[384,logseq____"^17logseq____",true,536870934]],[logseq____"^15logseq____",[384,logseq____"^;logseq____",logseq____"~u6531e478-50a8-4a3b-afe8-f2ad96a30244logseq____",536870934]]]]]]"</script>
+ <script>window.logseq_db="[logseq____"~#datascript/DBlogseq____",[logseq____"^ logseq____",logseq____"~:schemalogseq____",[logseq____"^ logseq____",logseq____"~:ast/versionlogseq____",[logseq____"^ logseq____"],logseq____"~:file/contentlogseq____",[logseq____"^ logseq____"],logseq____"~:block/properties-text-valueslogseq____",[logseq____"^ logseq____"],logseq____"~:block/aliaslogseq____",[logseq____"^ logseq____",logseq____"~:db/valueTypelogseq____",logseq____"~:db.type/reflogseq____",logseq____"~:db/cardinalitylogseq____",logseq____"~:db.cardinality/manylogseq____"],logseq____"~:block/pre-block?logseq____",[logseq____"^ logseq____"],logseq____"~:block/uuidlogseq____",[logseq____"^ logseq____",logseq____"~:db/uniquelogseq____",logseq____"~:db.unique/identitylogseq____"],logseq____"~:block/prioritylogseq____",[logseq____"^ logseq____"],logseq____"~:block/propertieslogseq____",[logseq____"^ logseq____"],logseq____"~:block/journal?logseq____",[logseq____"^ logseq____"],logseq____"~:block/namespacelogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____"],logseq____"~:block/updated-atlogseq____",[logseq____"^ logseq____"],logseq____"~:block/repeated?logseq____",[logseq____"^ logseq____"],logseq____"~:db/typelogseq____",[logseq____"^ logseq____"],logseq____"~:file/handlelogseq____",[logseq____"^ logseq____"],logseq____"~:block/leftlogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"~:db/indexlogseq____",true],logseq____"~:block/refslogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^8logseq____",logseq____"^9logseq____"],logseq____"~:block/scheduledlogseq____",[logseq____"^ logseq____"],logseq____"~:block/properties-orderlogseq____",[logseq____"^ logseq____"],logseq____"~:block/created-atlogseq____",[logseq____"^ logseq____"],logseq____"~:block/deadlinelogseq____",[logseq____"^ logseq____"],logseq____"~:block/collapsed?logseq____",[logseq____"^ logseq____",logseq____"^Glogseq____",true],logseq____"~:block/journal-daylogseq____",[logseq____"^ logseq____"],logseq____"~:block/formatlogseq____",[logseq____"^ logseq____"],logseq____"~:block/tagslogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^8logseq____",logseq____"^9logseq____"],logseq____"~:block/contentlogseq____",[logseq____"^ logseq____"],logseq____"~:recent/pageslogseq____",[logseq____"^ logseq____"],logseq____"~:block/macroslogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^8logseq____",logseq____"^9logseq____"],logseq____"~:db/identlogseq____",[logseq____"^ logseq____",logseq____"^logseq____<logseq____",logseq____"^=logseq____"],logseq____"~:block/path-refslogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^8logseq____",logseq____"^9logseq____"],logseq____"~:block/parentlogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^Glogseq____",true],logseq____"~:block/typelogseq____",[logseq____"^ logseq____"],logseq____"~:block/pagelogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____",logseq____"^Glogseq____",true],logseq____"~:block/namelogseq____",[logseq____"^ logseq____",logseq____"^logseq____<logseq____",logseq____"^=logseq____"],logseq____"~:file/pathlogseq____",[logseq____"^ logseq____",logseq____"^logseq____<logseq____",logseq____"^=logseq____"],logseq____"~:block/filelogseq____",[logseq____"^ logseq____",logseq____"^6logseq____",logseq____"^7logseq____"],logseq____"~:block/markerlogseq____",[logseq____"^ logseq____"],logseq____"~:block/original-namelogseq____",[logseq____"^ logseq____",logseq____"^logseq____<logseq____",logseq____"^=logseq____"],logseq____"~:schema/versionlogseq____",[logseq____"^ logseq____"]],logseq____"~:datomslogseq____",[logseq____"~#listlogseq____",[[logseq____"~#datascript/Datomlogseq____",[1,logseq____"^12logseq____",2,536870913]],[logseq____"^15logseq____",[2,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[2,logseq____"^Ylogseq____",logseq____"cardlogseq____",536870913]],[logseq____"^15logseq____",[2,logseq____"^11logseq____",logseq____"cardlogseq____",536870913]],[logseq____"^15logseq____",[2,logseq____"^;logseq____",logseq____"~udd9925ee-b311-4df7-bae9-a2c08a475641logseq____",536870914]],[logseq____"^15logseq____",[3,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[3,logseq____"^Ylogseq____",logseq____"canceledlogseq____",536870914]],[logseq____"^15logseq____",[3,logseq____"^11logseq____",logseq____"CANCELEDlogseq____",536870914]],[logseq____"^15logseq____",[3,logseq____"^;logseq____",logseq____"~u1e504364-1563-433f-9dfe-f3a65fb9714dlogseq____",536870914]],[logseq____"^15logseq____",[4,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[4,logseq____"^Ylogseq____",logseq____"todologseq____",536870914]],[logseq____"^15logseq____",[4,logseq____"^11logseq____",logseq____"TODOlogseq____",536870914]],[logseq____"^15logseq____",[4,logseq____"^;logseq____",logseq____"~ue3eeb59b-f228-49d4-a8d9-5c5877aeec26logseq____",536870914]],[logseq____"^15logseq____",[5,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[5,logseq____"^Ylogseq____",logseq____"nowlogseq____",536870914]],[logseq____"^15logseq____",[5,logseq____"^11logseq____",logseq____"NOWlogseq____",536870914]],[logseq____"^15logseq____",[5,logseq____"^;logseq____",logseq____"~u3133d6c0-e878-4ef5-a2b7-fcbbe4ec2e19logseq____",536870914]],[logseq____"^15logseq____",[6,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[6,logseq____"^Ylogseq____",logseq____"laterlogseq____",536870914]],[logseq____"^15logseq____",[6,logseq____"^11logseq____",logseq____"LATERlogseq____",536870914]],[logseq____"^15logseq____",[6,logseq____"^;logseq____",logseq____"~u0e107195-a071-4126-adfc-26aa678e948flogseq____",536870914]],[logseq____"^15logseq____",[7,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[7,logseq____"^Ylogseq____",logseq____"donelogseq____",536870914]],[logseq____"^15logseq____",[7,logseq____"^11logseq____",logseq____"DONElogseq____",536870914]],[logseq____"^15logseq____",[7,logseq____"^;logseq____",logseq____"~ud8b5e733-54e2-4984-82dd-e501ea294b42logseq____",536870914]],[logseq____"^15logseq____",[8,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[8,logseq____"^Ylogseq____",logseq____"doinglogseq____",536870914]],[logseq____"^15logseq____",[8,logseq____"^11logseq____",logseq____"DOINGlogseq____",536870914]],[logseq____"^15logseq____",[8,logseq____"^;logseq____",logseq____"~u4a8c6475-8e8d-4e90-a127-bd9e49ef5fc3logseq____",536870914]],[logseq____"^15logseq____",[9,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[9,logseq____"^Ylogseq____",logseq____"in-progresslogseq____",536870914]],[logseq____"^15logseq____",[9,logseq____"^11logseq____",logseq____"IN-PROGRESSlogseq____",536870914]],[logseq____"^15logseq____",[9,logseq____"^;logseq____",logseq____"~u4da0d3ea-4045-44b4-a99d-c3f4c90389f9logseq____",536870914]],[logseq____"^15logseq____",[10,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[10,logseq____"^Ylogseq____",logseq____"clogseq____",536870914]],[logseq____"^15logseq____",[10,logseq____"^11logseq____",logseq____"Clogseq____",536870914]],[logseq____"^15logseq____",[10,logseq____"^;logseq____",logseq____"~u40fa55f1-e160-43a7-98a3-b51421ae0d99logseq____",536870914]],[logseq____"^15logseq____",[11,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[11,logseq____"^Ylogseq____",logseq____"blogseq____",536870914]],[logseq____"^15logseq____",[11,logseq____"^11logseq____",logseq____"Blogseq____",536870914]],[logseq____"^15logseq____",[11,logseq____"^;logseq____",logseq____"~u5bd13677-ddd7-4dee-a453-bcc88fda543elogseq____",536870914]],[logseq____"^15logseq____",[12,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[12,logseq____"^Ylogseq____",logseq____"contentslogseq____",536870914]],[logseq____"^15logseq____",[12,logseq____"^11logseq____",logseq____"contentslogseq____",536870917]],[logseq____"^15logseq____",[12,logseq____"^;logseq____",logseq____"~u6535b15c-51d5-4ffa-8e4e-43639e7e7c65logseq____",536870917]],[logseq____"^15logseq____",[13,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[13,logseq____"^Ylogseq____",logseq____"waitinglogseq____",536870914]],[logseq____"^15logseq____",[13,logseq____"^11logseq____",logseq____"WAITINGlogseq____",536870914]],[logseq____"^15logseq____",[13,logseq____"^;logseq____",logseq____"~u62d3c0c9-a15f-4d84-a228-0490515a5697logseq____",536870914]],[logseq____"^15logseq____",[14,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[14,logseq____"^Ylogseq____",logseq____"favoriteslogseq____",536870914]],[logseq____"^15logseq____",[14,logseq____"^11logseq____",logseq____"Favoriteslogseq____",536870914]],[logseq____"^15logseq____",[14,logseq____"^;logseq____",logseq____"~u7ce7d695-2aa9-493b-8946-651e0b917a99logseq____",536870914]],[logseq____"^15logseq____",[15,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[15,logseq____"^Ylogseq____",logseq____"alogseq____",536870914]],[logseq____"^15logseq____",[15,logseq____"^11logseq____",logseq____"Alogseq____",536870914]],[logseq____"^15logseq____",[15,logseq____"^;logseq____",logseq____"~uecaea548-f1e8-4e89-8006-b6ac1014bceblogseq____",536870914]],[logseq____"^15logseq____",[16,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[16,logseq____"^Ylogseq____",logseq____"cancelledlogseq____",536870914]],[logseq____"^15logseq____",[16,logseq____"^11logseq____",logseq____"CANCELLEDlogseq____",536870914]],[logseq____"^15logseq____",[16,logseq____"^;logseq____",logseq____"~u6c7c18ea-b683-4940-8bc2-86145a4fbf76logseq____",536870914]],[logseq____"^15logseq____",[17,logseq____"^@logseq____",false,536870914]],[logseq____"^15logseq____",[17,logseq____"^Ylogseq____",logseq____"waitlogseq____",536870914]],[logseq____"^15logseq____",[17,logseq____"^11logseq____",logseq____"WAITlogseq____",536870914]],[logseq____"^15logseq____",[17,logseq____"^;logseq____",logseq____"~uf3fb6b73-6dde-4899-bdd4-56eb963c8d07logseq____",536870914]],[logseq____"^15logseq____",[21,logseq____"^Qlogseq____",logseq____"logseq____",536870917]],[logseq____"^15logseq____",[21,logseq____"^Ologseq____",logseq____"~:markdownlogseq____",536870917]],[logseq____"^15logseq____",[21,logseq____"^Flogseq____",12,536870917]],[logseq____"^15logseq____",[21,logseq____"^Xlogseq____",12,536870917]],[logseq____"^15logseq____",[21,logseq____"^Vlogseq____",12,536870917]],[logseq____"^15logseq____",[21,logseq____"^Ulogseq____",12,536870917]],[logseq____"^15logseq____",[21,logseq____"~:block/unorderedlogseq____",true,536870917]],[logseq____"^15logseq____",[21,logseq____"^;logseq____",logseq____"~u6535b15c-8810-45c9-b8d0-abbf6756329alogseq____",536870917]],[logseq____"^15logseq____",[24,logseq____"^Klogseq____",1698017628091,536870919]],[logseq____"^15logseq____",[24,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[24,logseq____"^@logseq____",false,536870919]],[logseq____"^15logseq____",[24,logseq____"^Ylogseq____",logseq____"auffrischung mathematiklogseq____",536870919]],[logseq____"^15logseq____",[24,logseq____"^11logseq____",logseq____"Auffrischung Mathematiklogseq____",536870919]],[logseq____"^15logseq____",[24,logseq____"^Blogseq____",1698017628091,536870919]],[logseq____"^15logseq____",[24,logseq____"^;logseq____",logseq____"~u6535b15d-d43b-4866-9662-15f2e06d97delogseq____",536870931]],[logseq____"^15logseq____",[25,logseq____"^Qlogseq____",logseq____"logseq____",536870919]],[logseq____"^15logseq____",[25,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[25,logseq____"^Flogseq____",24,536870919]],[logseq____"^15logseq____",[25,logseq____"^Xlogseq____",24,536870919]],[logseq____"^15logseq____",[25,logseq____"^Vlogseq____",24,536870919]],[logseq____"^15logseq____",[25,logseq____"^Ulogseq____",24,536870919]],[logseq____"^15logseq____",[25,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[25,logseq____"^;logseq____",logseq____"~u6535b15c-bed2-4b7d-9531-1dc62dc58cc2logseq____",536870919]],[logseq____"^15logseq____",[27,logseq____"^Klogseq____",1698017628344,536870920]],[logseq____"^15logseq____",[27,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[27,logseq____"^Ylogseq____",logseq____"quadratische ergänzunglogseq____",536870920]],[logseq____"^15logseq____",[27,logseq____"^11logseq____",logseq____"Quadratische Ergänzunglogseq____",536870920]],[logseq____"^15logseq____",[27,logseq____"^Blogseq____",1698017628344,536870920]],[logseq____"^15logseq____",[27,logseq____"^;logseq____",logseq____"~u6535b15c-eaed-4614-a351-59cbaa69e02blogseq____",536870920]],[logseq____"^15logseq____",[28,logseq____"^Klogseq____",1698017628337,536870920]],[logseq____"^15logseq____",[28,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[28,logseq____"^Ylogseq____",logseq____"potenzenlogseq____",536870920]],[logseq____"^15logseq____",[28,logseq____"^11logseq____",logseq____"Potenzenlogseq____",536870920]],[logseq____"^15logseq____",[28,logseq____"^Blogseq____",1698017628337,536870920]],[logseq____"^15logseq____",[28,logseq____"^;logseq____",logseq____"~u6535b15c-e978-4a18-8464-61cd7cb979cdlogseq____",536870920]],[logseq____"^15logseq____",[29,logseq____"^Klogseq____",1698017628327,536870920]],[logseq____"^15logseq____",[29,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[29,logseq____"^Ylogseq____",logseq____"pascalsches dreiecklogseq____",536870920]],[logseq____"^15logseq____",[29,logseq____"^11logseq____",logseq____"Pascalsches Dreiecklogseq____",536870920]],[logseq____"^15logseq____",[29,logseq____"^Blogseq____",1698017628327,536870920]],[logseq____"^15logseq____",[29,logseq____"^;logseq____",logseq____"~u6535b15c-942c-4a61-9e1c-16ed10d3ab73logseq____",536870920]],[logseq____"^15logseq____",[30,logseq____"^Klogseq____",1698017628342,536870920]],[logseq____"^15logseq____",[30,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[30,logseq____"^Ylogseq____",logseq____"quadratische gleichungenlogseq____",536870920]],[logseq____"^15logseq____",[30,logseq____"^11logseq____",logseq____"Quadratische Gleichungenlogseq____",536870920]],[logseq____"^15logseq____",[30,logseq____"^Blogseq____",1698017628342,536870920]],[logseq____"^15logseq____",[30,logseq____"^;logseq____",logseq____"~u6535b15c-8d62-4286-8ada-a1a7d0cd5afdlogseq____",536870920]],[logseq____"^15logseq____",[31,logseq____"^Klogseq____",1698017628349,536870920]],[logseq____"^15logseq____",[31,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[31,logseq____"^Ylogseq____",logseq____"wurzelgleichunglogseq____",536870920]],[logseq____"^15logseq____",[31,logseq____"^11logseq____",logseq____"Wurzelgleichunglogseq____",536870920]],[logseq____"^15logseq____",[31,logseq____"^Blogseq____",1698017628349,536870920]],[logseq____"^15logseq____",[31,logseq____"^;logseq____",logseq____"~u6535b15c-2224-46aa-bd41-5eadb27d8ed9logseq____",536870920]],[logseq____"^15logseq____",[32,logseq____"^Klogseq____",1698017628322,536870920]],[logseq____"^15logseq____",[32,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[32,logseq____"^Ylogseq____",logseq____"logarithmenlogseq____",536870920]],[logseq____"^15logseq____",[32,logseq____"^11logseq____",logseq____"Logarithmenlogseq____",536870920]],[logseq____"^15logseq____",[32,logseq____"^Blogseq____",1698017628322,536870920]],[logseq____"^15logseq____",[32,logseq____"^;logseq____",logseq____"~u6535b15d-8bc3-42da-85dc-67056a04c341logseq____",536870925]],[logseq____"^15logseq____",[33,logseq____"^Klogseq____",1698017628335,536870920]],[logseq____"^15logseq____",[33,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[33,logseq____"^Ylogseq____",logseq____"binomialkoeffizientlogseq____",536870920]],[logseq____"^15logseq____",[33,logseq____"^11logseq____",logseq____"Binomialkoeffizientlogseq____",536870920]],[logseq____"^15logseq____",[33,logseq____"^Blogseq____",1698017628335,536870920]],[logseq____"^15logseq____",[33,logseq____"^;logseq____",logseq____"~u6535b15c-f76b-4f52-968e-54fecc969501logseq____",536870920]],[logseq____"^15logseq____",[34,logseq____"^Klogseq____",1698017628321,536870920]],[logseq____"^15logseq____",[34,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[34,logseq____"^Ylogseq____",logseq____"gleichungenlogseq____",536870920]],[logseq____"^15logseq____",[34,logseq____"^11logseq____",logseq____"Gleichungenlogseq____",536870920]],[logseq____"^15logseq____",[34,logseq____"^Blogseq____",1698017628321,536870920]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u6535b15c-3da5-4c08-90d5-2b819defd185logseq____",536870920]],[logseq____"^15logseq____",[35,logseq____"^Klogseq____",1698017628325,536870920]],[logseq____"^15logseq____",[35,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[35,logseq____"^Ylogseq____",logseq____"binomische formelnlogseq____",536870920]],[logseq____"^15logseq____",[35,logseq____"^11logseq____",logseq____"Binomische Formelnlogseq____",536870920]],[logseq____"^15logseq____",[35,logseq____"^Blogseq____",1698017628325,536870920]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u6535b15c-07cb-45e5-81b4-6f23fd745979logseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^Klogseq____",1698017628345,536870920]],[logseq____"^15logseq____",[36,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[36,logseq____"^Ylogseq____",logseq____"beispielelogseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^11logseq____",logseq____"Beispielelogseq____",536870920]],[logseq____"^15logseq____",[36,logseq____"^Blogseq____",1698017628345,536870920]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u6535b15d-844f-4065-b9ca-81b12d4b2537logseq____",536870924]],[logseq____"^15logseq____",[37,logseq____"^Klogseq____",1698017628324,536870920]],[logseq____"^15logseq____",[37,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[37,logseq____"^Ylogseq____",logseq____"trigonometrielogseq____",536870920]],[logseq____"^15logseq____",[37,logseq____"^11logseq____",logseq____"Trigonometrielogseq____",536870920]],[logseq____"^15logseq____",[37,logseq____"^Blogseq____",1698017628324,536870920]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u6535b15c-1eb5-43cb-ad9e-115cab518ae7logseq____",536870920]],[logseq____"^15logseq____",[38,logseq____"^Klogseq____",1698017628339,536870920]],[logseq____"^15logseq____",[38,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[38,logseq____"^Ylogseq____",logseq____"wurzelnlogseq____",536870920]],[logseq____"^15logseq____",[38,logseq____"^11logseq____",logseq____"Wurzelnlogseq____",536870920]],[logseq____"^15logseq____",[38,logseq____"^Blogseq____",1698017628339,536870920]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u6535b15c-7cde-4908-8ead-b20d58272b79logseq____",536870920]],[logseq____"^15logseq____",[39,logseq____"^Klogseq____",1698017628336,536870920]],[logseq____"^15logseq____",[39,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[39,logseq____"^Ylogseq____",logseq____"pascalsche dreiecklogseq____",536870920]],[logseq____"^15logseq____",[39,logseq____"^11logseq____",logseq____"Pascalsche Dreiecklogseq____",536870920]],[logseq____"^15logseq____",[39,logseq____"^Blogseq____",1698017628336,536870920]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u6535b15c-1fc2-467e-9022-9ac67947ad56logseq____",536870920]],[logseq____"^15logseq____",[40,logseq____"^Klogseq____",1698017628341,536870920]],[logseq____"^15logseq____",[40,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[40,logseq____"^Ylogseq____",logseq____"rationalmachenlogseq____",536870920]],[logseq____"^15logseq____",[40,logseq____"^11logseq____",logseq____"Rationalmachenlogseq____",536870920]],[logseq____"^15logseq____",[40,logseq____"^Blogseq____",1698017628341,536870920]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u6535b15c-b858-4d41-8270-d6e3579fabb4logseq____",536870920]],[logseq____"^15logseq____",[41,logseq____"^Klogseq____",1698017628337,536870920]],[logseq____"^15logseq____",[41,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[41,logseq____"^Ylogseq____",logseq____"auffrischung mathematik/23-10-04logseq____",536870920]],[logseq____"^15logseq____",[41,logseq____"^Alogseq____",24,536870920]],[logseq____"^15logseq____",[41,logseq____"^11logseq____",logseq____"Auffrischung Mathematik/23-10-04logseq____",536870920]],[logseq____"^15logseq____",[41,logseq____"^Blogseq____",1698017628337,536870920]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u6535b15c-6062-4b31-9cc4-7e3ab7e56f96logseq____",536870920]],[logseq____"^15logseq____",[42,logseq____"^Klogseq____",1698017628345,536870920]],[logseq____"^15logseq____",[42,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[42,logseq____"^Ylogseq____",logseq____"satz von vietalogseq____",536870920]],[logseq____"^15logseq____",[42,logseq____"^11logseq____",logseq____"Satz von Vietalogseq____",536870920]],[logseq____"^15logseq____",[42,logseq____"^Blogseq____",1698017628345,536870920]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u6535b15c-a110-458e-bc75-5ab9f11a3364logseq____",536870920]],[logseq____"^15logseq____",[43,logseq____"^Klogseq____",1698017628339,536870920]],[logseq____"^15logseq____",[43,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[43,logseq____"^Ylogseq____",logseq____"fixmelogseq____",536870920]],[logseq____"^15logseq____",[43,logseq____"^11logseq____",logseq____"FIXMElogseq____",536870920]],[logseq____"^15logseq____",[43,logseq____"^Blogseq____",1698017628339,536870920]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u6535b15d-cb77-4dfb-8e82-afd717e8c1a3logseq____",536870924]],[logseq____"^15logseq____",[44,logseq____"^Klogseq____",1698017628343,536870920]],[logseq____"^15logseq____",[44,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[44,logseq____"^Ylogseq____",logseq____"pq-formellogseq____",536870920]],[logseq____"^15logseq____",[44,logseq____"^11logseq____",logseq____"pq-Formellogseq____",536870920]],[logseq____"^15logseq____",[44,logseq____"^Blogseq____",1698017628343,536870920]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u6535b15c-18a3-4a6c-9d8a-001a2e5b1e84logseq____",536870920]],[logseq____"^15logseq____",[45,logseq____"^Klogseq____",1698017628318,536870920]],[logseq____"^15logseq____",[45,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[45,logseq____"^Ylogseq____",logseq____"linkslogseq____",536870920]],[logseq____"^15logseq____",[45,logseq____"^11logseq____",logseq____"Linkslogseq____",536870920]],[logseq____"^15logseq____",[45,logseq____"^Blogseq____",1698017628318,536870920]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u6535b15c-175e-4718-866b-d1acf62457e9logseq____",536870920]],[logseq____"^15logseq____",[46,logseq____"^Klogseq____",1698017628340,536870920]],[logseq____"^15logseq____",[46,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[46,logseq____"^Ylogseq____",logseq____"nennerlogseq____",536870920]],[logseq____"^15logseq____",[46,logseq____"^11logseq____",logseq____"Nennerlogseq____",536870920]],[logseq____"^15logseq____",[46,logseq____"^Blogseq____",1698017628340,536870920]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u6535b15c-2e1f-4379-83ce-a500035f5955logseq____",536870920]],[logseq____"^15logseq____",[47,logseq____"^Klogseq____",1698017628319,536870920]],[logseq____"^15logseq____",[47,logseq____"^@logseq____",false,536870920]],[logseq____"^15logseq____",[47,logseq____"^Ylogseq____",logseq____"wolframalphalogseq____",536870920]],[logseq____"^15logseq____",[47,logseq____"^11logseq____",logseq____"Wolframalphalogseq____",536870920]],[logseq____"^15logseq____",[47,logseq____"^Blogseq____",1698017628319,536870920]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u6535b15c-f421-4dfc-b854-4580b740ea91logseq____",536870920]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870920]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",90,536870920]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",90,536870920]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[48,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",1],536870920]],[logseq____"^15logseq____",[48,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[48,logseq____"^Hlogseq____",28,536870920]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u6535b15c-8e7a-43af-9e03-1d574c29d109logseq____",536870920]],[logseq____"^15logseq____",[49,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870920]],[logseq____"^15logseq____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",75,536870920]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[49,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[49,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[49,logseq____"^Hlogseq____",38,536870920]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u6535b15c-0723-4b1f-abc3-d1e418aac7calogseq____",536870920]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870920]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",54,536870920]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[50,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u6535b15c-6ee9-42e2-a001-3abcd643ad92logseq____",536870920]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&=a^2-b^2\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",99,536870920]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",99,536870920]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u6535b15c-a537-4b94-803c-69840c4aaa54logseq____",536870920]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&=x^2\\\\\\\\\\ny^2-34y+225logseq____&=0\\\\\\\\\\ny_{1,2}logseq____&=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&\\\\rightarrow logseq____&x_1=5;logseq____&x_2=-5\\\\\\\\\\nx^2=9logseq____&\\\\rightarrow logseq____&x_1=3;logseq____&x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",57,536870920]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",105,536870920]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[52,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u6535b15c-44ee-4707-82c4-8a046bb81768logseq____",536870920]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&=a^2+2ab+b^2logseq____&,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&=a^2-2ab+b^2logseq____&,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&=a^2-b^2logseq____&,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",69,536870920]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",69,536870920]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u6535b15c-8b04-4fb6-a3a7-16bbd9c3b689logseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",48,536870920]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",90,536870920]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[54,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[54,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",38,536870920]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u6535b15c-8139-4526-8096-acaf816dc1f4logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",75,536870920]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",75,536870920]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",32,536870920]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u6535b15c-c7c9-4b3d-9561-89b1feef9439logseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",63,536870920]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",63,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",46,536870920]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6535b15c-b747-4a0d-8658-bae45eb49967logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0 logseq____&logseq____& \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&=-p logseq____&logseq____& x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",71,536870920]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",105,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",42,536870920]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u6535b15c-439e-494c-9221-1f56fdcc06d0logseq____",536870920]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870920]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",72,536870920]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[58,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[58,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",28,536870920]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u6535b15c-c9f4-4511-ac22-929ead0e5a1flogseq____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",61,536870920]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u6535b15c-34c4-4728-b78b-a7eee3bd9b1blogseq____",536870920]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&= p logseq____&, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&=0\\\\\\\\\\nx^2-7x+12logseq____&=0\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",100,536870920]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",100,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6535b15c-f27d-4875-9df2-bc12828a46e0logseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",76,536870920]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u6535b15c-8d6c-4f3a-b813-ff01ff6f7178logseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",97,536870920]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",77,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",31,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u6535b15c-1fa7-4e3d-abc7-ddfe4fc10a7blogseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"## [[Rationalmachen]] des [[Nenner]]slogseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",59,536870920]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",46,536870920]],[logseq____"^15logseq____",[63,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[63,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",40,536870920]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",46,536870920]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6535b15c-1771-40c9-a1a8-d4c99dc75f2dlogseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&, a,b,logseq____>0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",102,536870920]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",102,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",46,536870920]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u6535b15c-b4f4-44f4-b450-da3f2cdb3098logseq____",536870920]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",53,536870920]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",69,536870920]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6535b15c-4346-4653-9058-7f278ef503bblogseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",83,536870920]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",61,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[66,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u6535b15c-501b-4ce0-beaa-5e67ed8dd56dlogseq____",536870920]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870920]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",93,536870920]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",79,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",33,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[67,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[67,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",33,536870920]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u6535b15c-359c-43d8-b4d1-5869c7512a95logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",95,536870920]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",95,536870920]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u6535b15c-d8a3-4c5d-83b3-109f9f48d1a9logseq____",536870920]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870920]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",95,536870920]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[69,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[69,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[69,logseq____"^Hlogseq____",35,536870920]],[logseq____"^15logseq____",[69,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[69,logseq____"^;logseq____",logseq____"~u6535b15c-820c-4d0a-ae3c-7694e3777fa3logseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Qlogseq____",logseq____"https://www.wolframalpha.comlogseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[70,logseq____"^Flogseq____",103,536870920]],[logseq____"^15logseq____",[70,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[70,logseq____"^Vlogseq____",103,536870920]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",45,536870920]],[logseq____"^15logseq____",[70,logseq____"^Ulogseq____",47,536870920]],[logseq____"^15logseq____",[70,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[70,logseq____"^;logseq____",logseq____"~u6535b15c-e37e-4427-9328-8a5c8d953e53logseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[71,logseq____"^Flogseq____",105,536870920]],[logseq____"^15logseq____",[71,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[71,logseq____"^Vlogseq____",105,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",27,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[71,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[71,logseq____"^Hlogseq____",27,536870920]],[logseq____"^15logseq____",[71,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[71,logseq____"^;logseq____",logseq____"~u6535b15c-b570-4aaf-8ce3-bf57b68ac877logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[72,logseq____"^Flogseq____",41,536870920]],[logseq____"^15logseq____",[72,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[72,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[72,logseq____"^Ulogseq____",45,536870920]],[logseq____"^15logseq____",[72,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[72,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[72,logseq____"^Hlogseq____",45,536870920]],[logseq____"^15logseq____",[72,logseq____"^17logseq____",false,536870920]],[logseq____"^15logseq____",[72,logseq____"^;logseq____",logseq____"~u6535b15c-9bb3-49f6-b97a-3aac6932a595logseq____",536870920]],[logseq____"^15logseq____",[73,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[73,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[73,logseq____"^Flogseq____",68,536870920]],[logseq____"^15logseq____",[73,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[73,logseq____"^Vlogseq____",95,536870920]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[73,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[73,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[73,logseq____"^;logseq____",logseq____"~u6535b15c-212e-43e1-b083-33e0ef19d8c4logseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[74,logseq____"^Flogseq____",73,536870920]],[logseq____"^15logseq____",[74,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[74,logseq____"^Vlogseq____",73,536870920]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[74,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[74,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[74,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[74,logseq____"^;logseq____",logseq____"~u6535b15c-ffa1-444d-a635-7e2534a0e72blogseq____",536870920]],[logseq____"^15logseq____",[75,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870920]],[logseq____"^15logseq____",[75,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[75,logseq____"^Flogseq____",58,536870920]],[logseq____"^15logseq____",[75,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[75,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",32,536870920]],[logseq____"^15logseq____",[75,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[75,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[75,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[75,logseq____"^Hlogseq____",32,536870920]],[logseq____"^15logseq____",[75,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[75,logseq____"^;logseq____",logseq____"~u6535b15c-00b6-4ed6-9cc1-f317668b93fblogseq____",536870920]],[logseq____"^15logseq____",[76,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[76,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[76,logseq____"^Flogseq____",50,536870920]],[logseq____"^15logseq____",[76,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[76,logseq____"^Vlogseq____",54,536870920]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[76,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[76,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[76,logseq____"^;logseq____",logseq____"~u6535b15c-a4de-4e57-879f-9ab757119d3alogseq____",536870920]],[logseq____"^15logseq____",[77,logseq____"^Qlogseq____",logseq____"# [[Wurzelgleichung]]logseq____",536870920]],[logseq____"^15logseq____",[77,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[77,logseq____"^Flogseq____",78,536870920]],[logseq____"^15logseq____",[77,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[77,logseq____"^Vlogseq____",90,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",31,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[77,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[77,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[77,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[77,logseq____"^Hlogseq____",31,536870920]],[logseq____"^15logseq____",[77,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[77,logseq____"^;logseq____",logseq____"~u6535b15c-384d-4ad3-bdf3-3ff2357d2b99logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Qlogseq____",logseq____"# [[Quadratische Gleichungen]]logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[78,logseq____"^Flogseq____",54,536870920]],[logseq____"^15logseq____",[78,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[78,logseq____"^Vlogseq____",90,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[78,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[78,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[78,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[78,logseq____"^Hlogseq____",30,536870920]],[logseq____"^15logseq____",[78,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[78,logseq____"^;logseq____",logseq____"~u6535b15c-6178-4d7a-b40d-921c89b5b032logseq____",536870920]],[logseq____"^15logseq____",[79,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870920]],[logseq____"^15logseq____",[79,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[79,logseq____"^Flogseq____",65,536870920]],[logseq____"^15logseq____",[79,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[79,logseq____"^Vlogseq____",69,536870920]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[79,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[79,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[79,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[79,logseq____"^Hlogseq____",29,536870920]],[logseq____"^15logseq____",[79,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[79,logseq____"^;logseq____",logseq____"~u6535b15c-2019-4b44-b805-899858a140e6logseq____",536870920]],[logseq____"^15logseq____",[80,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nax^2+bx+clogseq____&=0logseq____&|:a\\\\quadlogseq____&a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&= 0\\\\\\\\\\nplogseq____&=\\\\frac ba,logseq____&q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&=0\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[80,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[80,logseq____"^Flogseq____",78,536870920]],[logseq____"^15logseq____",[80,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[80,logseq____"^Vlogseq____",78,536870920]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[80,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[80,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[80,logseq____"^;logseq____",logseq____"~u6535b15c-2c0c-4dd5-b507-fd7244089356logseq____",536870920]],[logseq____"^15logseq____",[81,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870920]],[logseq____"^15logseq____",[81,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[81,logseq____"^Flogseq____",94,536870920]],[logseq____"^15logseq____",[81,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[81,logseq____"^Vlogseq____",93,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[81,logseq____"^Ulogseq____",43,536870920]],[logseq____"^15logseq____",[81,logseq____"^Hlogseq____",43,536870920]],[logseq____"^15logseq____",[81,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[81,logseq____"^;logseq____",logseq____"~u6535b15c-075b-4c78-8d15-cd9e8b338bf3logseq____",536870920]],[logseq____"^15logseq____",[82,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870920]],[logseq____"^15logseq____",[82,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[82,logseq____"^Flogseq____",88,536870920]],[logseq____"^15logseq____",[82,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[82,logseq____"^Vlogseq____",88,536870920]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[82,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[82,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[82,logseq____"^;logseq____",logseq____"~u6535b15c-d948-4f99-9460-9f1d2104530clogseq____",536870920]],[logseq____"^15logseq____",[83,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{y^2}=\\\\left|y\\\\right|\\\\\\\\\\n\\\\sqrt[5]{a\\\\sqrt[3]a}=\\\\sqrt[5]{\\\\sqrt[3]{a^3}\\\\sqrt[3]a}\\nlogseq____&=\\\\sqrt[5]{\\\\sqrt[3]{a^4}}\\n=\\\\sqrt[5]{a^\\\\frac43}\\n=a^{\\\\frac43\\\\frac15}=a^\\\\frac4{15}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",61,536870920]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",61,536870920]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u6535b15c-167e-45e5-8f4b-9ac0c9c6cfcblogseq____",536870920]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",58,536870920]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",58,536870920]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",34,536870920]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",34,536870920]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u6535b15c-8779-4878-90bc-5b6f9dd09840logseq____",536870920]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",96,536870920]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",49,536870920]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u6535b15c-1ca1-4c47-b928-152fdad246e2logseq____",536870920]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870920]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",67,536870920]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",67,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",33,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",39,536870920]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[86,logseq____"^Hlogseq____",39,536870920]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u6535b15c-e5fc-4a44-949f-d133fb3a12adlogseq____",536870920]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",101,536870920]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",101,536870920]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u6535b15c-8232-430a-8712-1b143c5d1fd7logseq____",536870920]],[logseq____"^15logseq____",[88,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",99,536870920]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",48,536870920]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u6535b15c-b147-446a-8215-a055bd044eaalogseq____",536870920]],[logseq____"^15logseq____",[89,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c} (a+b)^0logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 \\\\\\\\\\n(a+b)^1logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^2logseq____&logseq____&logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 2 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^3logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 3 logseq____&logseq____& 3 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^4logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 4 logseq____&logseq____& 6 logseq____&logseq____& 4 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^5logseq____&logseq____&logseq____& 1 logseq____&logseq____& 5 logseq____&logseq____& 10 logseq____&logseq____& 10 logseq____&logseq____& 5 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^6logseq____&logseq____& 1 logseq____&logseq____& 6 logseq____&logseq____& 15 logseq____&logseq____& 20 logseq____&logseq____& 15 logseq____&logseq____& 6 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^7logseq____&1 logseq____&logseq____& 7 logseq____&logseq____&21 logseq____&logseq____& 35 logseq____&logseq____& 35 logseq____&logseq____& \\\\cdots\\\\end{array}logseq____",536870920]],[logseq____"^15logseq____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",79,536870920]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",79,536870920]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u6535b15c-a909-4bf4-be0d-04ad8283feaclogseq____",536870920]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870920]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",69,536870920]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[90,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[90,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[90,logseq____"^Hlogseq____",28,536870920]],[logseq____"^15logseq____",[90,logseq____"^Hlogseq____",38,536870920]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u6535b15c-74b6-45f3-8519-a3234ccf447dlogseq____",536870920]],[logseq____"^15logseq____",[91,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\na^nlogseq____&=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____& a,blogseq____>0\\\\\\\\\\na^2b^2logseq____&=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&=a^{nm}\\\\\\\\\\na^0logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",48,536870920]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",48,536870920]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u6535b15c-2219-4d77-9609-5b40657c89aflogseq____",536870920]],[logseq____"^15logseq____",[92,logseq____"^Qlogseq____",logseq____"logseq____",536870920]],[logseq____"^15logseq____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",84,536870920]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",58,536870920]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u6535b15c-f32c-4d3f-a9ad-21ceeda0ef76logseq____",536870920]],[logseq____"^15logseq____",[93,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870920]],[logseq____"^15logseq____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",89,536870920]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",79,536870920]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[93,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u6535b15c-78a2-4c27-9ec3-067f025b0787logseq____",536870920]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(2x+y)^4logseq____&=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5logseq____&=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",93,536870920]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",93,536870920]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u6535b15c-0300-4d97-8071-69091445b108logseq____",536870920]],[logseq____"^15logseq____",[95,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870920]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",101,536870920]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",37,536870920]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[95,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[95,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[95,logseq____"^Hlogseq____",37,536870920]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u6535b15c-d04e-4be9-8756-30def9f2b405logseq____",536870920]],[logseq____"^15logseq____",[96,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[96,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[96,logseq____"^Flogseq____",49,536870920]],[logseq____"^15logseq____",[96,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[96,logseq____"^Vlogseq____",49,536870920]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[96,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[96,logseq____"^;logseq____",logseq____"~u6535b15c-a11c-4214-8c04-c184c3a23abflogseq____",536870920]],[logseq____"^15logseq____",[97,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{a+5}-\\\\sqrt{x+3}logseq____&=2\\\\sqrt(x+1) logseq____&|logseq____&()^2\\\\\\\\\\n\\\\left(\\\\sqrt{x+5}-\\\\sqrt{x+3}\\\\right)^2logseq____&=4(x+1)\\\\\\\\\\n(x+5)-2\\\\sqrt{x+5}\\\\sqrt{x+3}+(x+3)logseq____&=4x+4logseq____&|logseq____&-(2x+8)\\\\\\\\\\n-2\\\\sqrt{(x+5)(x+3)}logseq____&=2x-4 logseq____&|logseq____&()^2\\\\\\\\\\n4(x+5)(x+3)logseq____&=4x^2-16x+16\\\\\\\\\\n4x^2+32x+60logseq____&=4x^2-16x+16logseq____&|logseq____&-4x^2+16x-16\\\\\\\\\\n48x+44logseq____&=0\\\\quad x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[97,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[97,logseq____"^Flogseq____",77,536870920]],[logseq____"^15logseq____",[97,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[97,logseq____"^Vlogseq____",77,536870920]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",31,536870920]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[97,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[97,logseq____"^;logseq____",logseq____"~u6535b15c-d021-40f8-9068-327f43e028d0logseq____",536870920]],[logseq____"^15logseq____",[98,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&= \\\\frac1{\\\\ln a}\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[98,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[98,logseq____"^Flogseq____",55,536870920]],[logseq____"^15logseq____",[98,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[98,logseq____"^Vlogseq____",75,536870920]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",32,536870920]],[logseq____"^15logseq____",[98,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[98,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[98,logseq____"^;logseq____",logseq____"~u6535b15c-4123-4a99-828b-51b56425279flogseq____",536870920]],[logseq____"^15logseq____",[99,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870920]],[logseq____"^15logseq____",[99,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[99,logseq____"^Flogseq____",91,536870920]],[logseq____"^15logseq____",[99,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[99,logseq____"^Vlogseq____",48,536870920]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[99,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[99,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[99,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[99,logseq____"^;logseq____",logseq____"~u6535b15c-5d68-4dde-940f-b8314b05160clogseq____",536870920]],[logseq____"^15logseq____",[100,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870920]],[logseq____"^15logseq____",[100,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[100,logseq____"^Flogseq____",57,536870920]],[logseq____"^15logseq____",[100,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[100,logseq____"^Vlogseq____",57,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[100,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[100,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[100,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[100,logseq____"^;logseq____",logseq____"~u6535b15c-1ad7-44fe-b908-d12698096e2alogseq____",536870920]],[logseq____"^15logseq____",[101,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870920]],[logseq____"^15logseq____",[101,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[101,logseq____"^Flogseq____",49,536870920]],[logseq____"^15logseq____",[101,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[101,logseq____"^Vlogseq____",41,536870920]],[logseq____"^15logseq____",[101,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[101,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870920]],[logseq____"^15logseq____",[101,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[101,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[101,logseq____"^;logseq____",logseq____"~u6535b15c-4278-43f5-8c4b-61e11c50bceflogseq____",536870920]],[logseq____"^15logseq____",[102,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870920]],[logseq____"^15logseq____",[102,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[102,logseq____"^Flogseq____",56,536870920]],[logseq____"^15logseq____",[102,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[102,logseq____"^Vlogseq____",63,536870920]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",36,536870920]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",40,536870920]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[102,logseq____"^Ulogseq____",46,536870920]],[logseq____"^15logseq____",[102,logseq____"^Hlogseq____",36,536870920]],[logseq____"^15logseq____",[102,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[102,logseq____"^;logseq____",logseq____"~u6535b15c-4168-46e3-8e3b-04fdcaaba179logseq____",536870920]],[logseq____"^15logseq____",[103,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870920]],[logseq____"^15logseq____",[103,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[103,logseq____"^Flogseq____",72,536870920]],[logseq____"^15logseq____",[103,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[103,logseq____"^Vlogseq____",72,536870920]],[logseq____"^15logseq____",[103,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[103,logseq____"^Ulogseq____",45,536870920]],[logseq____"^15logseq____",[103,logseq____"^Ulogseq____",47,536870920]],[logseq____"^15logseq____",[103,logseq____"^Hlogseq____",47,536870920]],[logseq____"^15logseq____",[103,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[103,logseq____"^;logseq____",logseq____"~u6535b15c-88ef-48ec-9b3c-ebe9924300fblogseq____",536870920]],[logseq____"^15logseq____",[104,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870920]],[logseq____"^15logseq____",[104,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[104,logseq____"^Flogseq____",86,536870920]],[logseq____"^15logseq____",[104,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[104,logseq____"^Vlogseq____",67,536870920]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",29,536870920]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",33,536870920]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[104,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[104,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[104,logseq____"^;logseq____",logseq____"~u6535b15c-9c64-461c-9955-b35986815ca4logseq____",536870920]],[logseq____"^15logseq____",[105,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870920]],[logseq____"^15logseq____",[105,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[105,logseq____"^Flogseq____",80,536870920]],[logseq____"^15logseq____",[105,logseq____"^Xlogseq____",41,536870920]],[logseq____"^15logseq____",[105,logseq____"^Vlogseq____",78,536870920]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",28,536870920]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",30,536870920]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",38,536870920]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",41,536870920]],[logseq____"^15logseq____",[105,logseq____"^Ulogseq____",44,536870920]],[logseq____"^15logseq____",[105,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[105,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[105,logseq____"^Hlogseq____",44,536870920]],[logseq____"^15logseq____",[105,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[105,logseq____"^;logseq____",logseq____"~u6535b15c-fefb-447d-844d-1419bf082c95logseq____",536870920]],[logseq____"^15logseq____",[107,logseq____"^Klogseq____",1698017628617,536870921]],[logseq____"^15logseq____",[107,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[107,logseq____"^Ylogseq____",logseq____"kreislogseq____",536870921]],[logseq____"^15logseq____",[107,logseq____"^11logseq____",logseq____"Kreislogseq____",536870921]],[logseq____"^15logseq____",[107,logseq____"^Blogseq____",1698017628617,536870921]],[logseq____"^15logseq____",[107,logseq____"^;logseq____",logseq____"~u6535b15c-2f34-4bc1-8527-6f1accb9c372logseq____",536870921]],[logseq____"^15logseq____",[108,logseq____"^Klogseq____",1698017628625,536870921]],[logseq____"^15logseq____",[108,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[108,logseq____"^Ylogseq____",logseq____"fester punktlogseq____",536870921]],[logseq____"^15logseq____",[108,logseq____"^11logseq____",logseq____"Fester Punktlogseq____",536870921]],[logseq____"^15logseq____",[108,logseq____"^Blogseq____",1698017628625,536870921]],[logseq____"^15logseq____",[108,logseq____"^;logseq____",logseq____"~u6535b15c-176d-4b2a-814c-35a1c17ee014logseq____",536870921]],[logseq____"^15logseq____",[109,logseq____"^Klogseq____",1698017628619,536870921]],[logseq____"^15logseq____",[109,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[109,logseq____"^Ylogseq____",logseq____"radiuslogseq____",536870921]],[logseq____"^15logseq____",[109,logseq____"^11logseq____",logseq____"Radiuslogseq____",536870921]],[logseq____"^15logseq____",[109,logseq____"^Blogseq____",1698017628619,536870921]],[logseq____"^15logseq____",[109,logseq____"^;logseq____",logseq____"~u6535b15c-0ed6-4af1-a63d-7a6497e4f969logseq____",536870921]],[logseq____"^15logseq____",[110,logseq____"^Klogseq____",1698017628615,536870921]],[logseq____"^15logseq____",[110,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[110,logseq____"^Ylogseq____",logseq____"fallunterscheidunglogseq____",536870921]],[logseq____"^15logseq____",[110,logseq____"^11logseq____",logseq____"Fallunterscheidunglogseq____",536870921]],[logseq____"^15logseq____",[110,logseq____"^Blogseq____",1698017628615,536870921]],[logseq____"^15logseq____",[110,logseq____"^;logseq____",logseq____"~u6535b15c-27c0-4fee-b79e-61a0a74f10dalogseq____",536870921]],[logseq____"^15logseq____",[111,logseq____"^Klogseq____",1698017628629,536870921]],[logseq____"^15logseq____",[111,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[111,logseq____"^Ylogseq____",logseq____"ellipselogseq____",536870921]],[logseq____"^15logseq____",[111,logseq____"^11logseq____",logseq____"Ellipselogseq____",536870921]],[logseq____"^15logseq____",[111,logseq____"^Blogseq____",1698017628629,536870921]],[logseq____"^15logseq____",[111,logseq____"^;logseq____",logseq____"~u6535b15c-28be-48a8-892a-2a443f0c9aeflogseq____",536870921]],[logseq____"^15logseq____",[112,logseq____"^Klogseq____",1698017628618,536870921]],[logseq____"^15logseq____",[112,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[112,logseq____"^Ylogseq____",logseq____"mittelpunktlogseq____",536870921]],[logseq____"^15logseq____",[112,logseq____"^11logseq____",logseq____"Mittelpunktlogseq____",536870921]],[logseq____"^15logseq____",[112,logseq____"^Blogseq____",1698017628618,536870921]],[logseq____"^15logseq____",[112,logseq____"^;logseq____",logseq____"~u6535b15c-32be-4db4-9289-ddf33a1001e2logseq____",536870921]],[logseq____"^15logseq____",[113,logseq____"^Klogseq____",1698017628622,536870921]],[logseq____"^15logseq____",[113,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[113,logseq____"^Ylogseq____",logseq____"konstantlogseq____",536870921]],[logseq____"^15logseq____",[113,logseq____"^11logseq____",logseq____"konstantlogseq____",536870921]],[logseq____"^15logseq____",[113,logseq____"^Blogseq____",1698017628622,536870921]],[logseq____"^15logseq____",[113,logseq____"^;logseq____",logseq____"~u6535b15c-e164-4850-aafb-81b08cec0c0dlogseq____",536870921]],[logseq____"^15logseq____",[114,logseq____"^Klogseq____",1698017628613,536870921]],[logseq____"^15logseq____",[114,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[114,logseq____"^Ylogseq____",logseq____"ungleichungenlogseq____",536870921]],[logseq____"^15logseq____",[114,logseq____"^11logseq____",logseq____"Ungleichungenlogseq____",536870921]],[logseq____"^15logseq____",[114,logseq____"^Blogseq____",1698017628613,536870921]],[logseq____"^15logseq____",[114,logseq____"^;logseq____",logseq____"~u6535b15d-526b-444f-a860-7b829ff7f90dlogseq____",536870930]],[logseq____"^15logseq____",[115,logseq____"^Klogseq____",1698017628625,536870921]],[logseq____"^15logseq____",[115,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[115,logseq____"^Ylogseq____",logseq____"brennpunktlogseq____",536870921]],[logseq____"^15logseq____",[115,logseq____"^11logseq____",logseq____"Brennpunktlogseq____",536870921]],[logseq____"^15logseq____",[115,logseq____"^Blogseq____",1698017628625,536870921]],[logseq____"^15logseq____",[115,logseq____"^;logseq____",logseq____"~u6535b15c-59af-416c-a793-d5145b51299clogseq____",536870921]],[logseq____"^15logseq____",[116,logseq____"^Klogseq____",1698017628630,536870921]],[logseq____"^15logseq____",[116,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[116,logseq____"^Ylogseq____",logseq____"asymptotelogseq____",536870921]],[logseq____"^15logseq____",[116,logseq____"^11logseq____",logseq____"Asymptotelogseq____",536870921]],[logseq____"^15logseq____",[116,logseq____"^Blogseq____",1698017628630,536870921]],[logseq____"^15logseq____",[116,logseq____"^;logseq____",logseq____"~u6535b15c-4f87-459e-83a7-8cfc8222f7dblogseq____",536870921]],[logseq____"^15logseq____",[117,logseq____"^Klogseq____",1698017628610,536870921]],[logseq____"^15logseq____",[117,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[117,logseq____"^Ylogseq____",logseq____"lösungsmengenlogseq____",536870921]],[logseq____"^15logseq____",[117,logseq____"^11logseq____",logseq____"Lösungsmengenlogseq____",536870921]],[logseq____"^15logseq____",[117,logseq____"^Blogseq____",1698017628610,536870921]],[logseq____"^15logseq____",[117,logseq____"^;logseq____",logseq____"~u6535b15c-c908-4047-bd42-52e804d9f69elogseq____",536870921]],[logseq____"^15logseq____",[118,logseq____"^Klogseq____",1698017628625,536870921]],[logseq____"^15logseq____",[118,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[118,logseq____"^Ylogseq____",logseq____"abstandlogseq____",536870921]],[logseq____"^15logseq____",[118,logseq____"^11logseq____",logseq____"Abstandlogseq____",536870921]],[logseq____"^15logseq____",[118,logseq____"^Blogseq____",1698017628625,536870921]],[logseq____"^15logseq____",[118,logseq____"^;logseq____",logseq____"~u6535b15c-1f89-4dc7-81b9-28b2589983dblogseq____",536870921]],[logseq____"^15logseq____",[119,logseq____"^Klogseq____",1698017628629,536870921]],[logseq____"^15logseq____",[119,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[119,logseq____"^Ylogseq____",logseq____"hyperbellogseq____",536870921]],[logseq____"^15logseq____",[119,logseq____"^11logseq____",logseq____"Hyperbellogseq____",536870921]],[logseq____"^15logseq____",[119,logseq____"^Blogseq____",1698017628629,536870921]],[logseq____"^15logseq____",[119,logseq____"^;logseq____",logseq____"~u6535b15c-35e2-4451-a0a3-3ce6309b4967logseq____",536870921]],[logseq____"^15logseq____",[120,logseq____"^Klogseq____",1698017628629,536870921]],[logseq____"^15logseq____",[120,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[120,logseq____"^Ylogseq____",logseq____"summelogseq____",536870921]],[logseq____"^15logseq____",[120,logseq____"^11logseq____",logseq____"Summelogseq____",536870921]],[logseq____"^15logseq____",[120,logseq____"^Blogseq____",1698017628629,536870921]],[logseq____"^15logseq____",[120,logseq____"^;logseq____",logseq____"~u6535b15c-2c24-4bab-902d-970484b9e2dalogseq____",536870921]],[logseq____"^15logseq____",[121,logseq____"^Klogseq____",1698017628613,536870921]],[logseq____"^15logseq____",[121,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[121,logseq____"^Ylogseq____",logseq____"betraglogseq____",536870921]],[logseq____"^15logseq____",[121,logseq____"^11logseq____",logseq____"Betraglogseq____",536870921]],[logseq____"^15logseq____",[121,logseq____"^Blogseq____",1698017628613,536870921]],[logseq____"^15logseq____",[121,logseq____"^;logseq____",logseq____"~u6535b15c-32de-4d35-9bdc-cd40612f0fc1logseq____",536870921]],[logseq____"^15logseq____",[122,logseq____"^Klogseq____",1698017628615,536870921]],[logseq____"^15logseq____",[122,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[122,logseq____"^Ylogseq____",logseq____"auffrischung mathematik/23-10-05logseq____",536870921]],[logseq____"^15logseq____",[122,logseq____"^Alogseq____",24,536870921]],[logseq____"^15logseq____",[122,logseq____"^11logseq____",logseq____"Auffrischung Mathematik/23-10-05logseq____",536870921]],[logseq____"^15logseq____",[122,logseq____"^Blogseq____",1698017628615,536870921]],[logseq____"^15logseq____",[122,logseq____"^;logseq____",logseq____"~u6535b15c-19a9-4bd0-8a35-be68b24a5b91logseq____",536870921]],[logseq____"^15logseq____",[123,logseq____"^Klogseq____",1698017628629,536870921]],[logseq____"^15logseq____",[123,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[123,logseq____"^Ylogseq____",logseq____"differenzlogseq____",536870921]],[logseq____"^15logseq____",[123,logseq____"^11logseq____",logseq____"Differenzlogseq____",536870921]],[logseq____"^15logseq____",[123,logseq____"^Blogseq____",1698017628629,536870921]],[logseq____"^15logseq____",[123,logseq____"^;logseq____",logseq____"~u6535b15c-b871-4db8-a125-f2899c4386eclogseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^Klogseq____",1698017628612,536870921]],[logseq____"^15logseq____",[124,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[124,logseq____"^Ylogseq____",logseq____"betragsungleichungenlogseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^11logseq____",logseq____"Betragsungleichungenlogseq____",536870921]],[logseq____"^15logseq____",[124,logseq____"^Blogseq____",1698017628612,536870921]],[logseq____"^15logseq____",[124,logseq____"^;logseq____",logseq____"~u6535b15c-e50b-415f-a54f-4cc26de5e847logseq____",536870921]],[logseq____"^15logseq____",[125,logseq____"^Klogseq____",1698017628626,536870921]],[logseq____"^15logseq____",[125,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[125,logseq____"^Ylogseq____",logseq____"punktelogseq____",536870921]],[logseq____"^15logseq____",[125,logseq____"^11logseq____",logseq____"Punktelogseq____",536870921]],[logseq____"^15logseq____",[125,logseq____"^Blogseq____",1698017628626,536870921]],[logseq____"^15logseq____",[125,logseq____"^;logseq____",logseq____"~u6535b15c-f7f8-4866-b2a7-6eb25b02a63alogseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Klogseq____",1698017628626,536870921]],[logseq____"^15logseq____",[126,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[126,logseq____"^Ylogseq____",logseq____"ebenenlogseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^11logseq____",logseq____"Ebenenlogseq____",536870921]],[logseq____"^15logseq____",[126,logseq____"^Blogseq____",1698017628626,536870921]],[logseq____"^15logseq____",[126,logseq____"^;logseq____",logseq____"~u6535b15c-63f2-42d1-8e3f-0fc4cb51ec78logseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Klogseq____",1698017628626,536870921]],[logseq____"^15logseq____",[127,logseq____"^@logseq____",false,536870921]],[logseq____"^15logseq____",[127,logseq____"^Ylogseq____",logseq____"mengenlogseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^11logseq____",logseq____"Mengenlogseq____",536870921]],[logseq____"^15logseq____",[127,logseq____"^Blogseq____",1698017628626,536870921]],[logseq____"^15logseq____",[127,logseq____"^;logseq____",logseq____"~u6535b15c-e7c3-4d6a-812d-38a4cbcef7aflogseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Qlogseq____",logseq____"a, b Halbachsen der Ellipselogseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[128,logseq____"^Flogseq____",133,536870921]],[logseq____"^15logseq____",[128,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[128,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[128,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[128,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[128,logseq____"^;logseq____",logseq____"~u6535b15c-c413-4392-8cab-18eded72d0c1logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[129,logseq____"^Flogseq____",144,536870921]],[logseq____"^15logseq____",[129,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[129,logseq____"^Vlogseq____",166,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[129,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[129,logseq____"^;logseq____",logseq____"~u6535b15c-bdc3-419a-b2be-7bc76a2b74cblogseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1a}\\\\quad x\\\\ge -2$\\n\\\\begin{align}\\n|x+2|logseq____&=x+2\\\\\\\\\\nx-3logseq____&\\\\le x+2 logseq____&|logseq____&+3-x\\\\\\\\\\n0logseq____&\\\\le5\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3,x\\\\ge-2,0\\\\le5\\\\right\\\\}=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3\\\\right\\\\}=[3,\\\\infty)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[130,logseq____"^Flogseq____",146,536870921]],[logseq____"^15logseq____",[130,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[130,logseq____"^Vlogseq____",172,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[130,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[130,logseq____"^;logseq____",logseq____"~u6535b15c-093a-44dc-84ed-72ff1e799ba8logseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Qlogseq____",logseq____"$\\\\text{Lösungsmenge der Gleichung }x^2+\\\\underbrace{4}_p x-\\\\underbrace{12}_q=0$\\n\\\\begin{align}\\nx_{1,2}logseq____&=\\\\frac{-p}2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\nlogseq____&=-2\\\\pm\\\\sqrt{\\\\frac{16}4-(-12)}\\\\\\\\\\nlogseq____&=-2\\\\pm4\\\\\\\\\\nLlogseq____&=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_\\\\text{Name}\\\\middle|\\\\underbrace{x^2+4x-12=0}_\\\\text{Eigenschaft}\\\\right\\\\}\\\\\\\\\\nLlogseq____&=\\\\left\\\\{2,-6\\\\right\\\\}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[131,logseq____"^Flogseq____",155,536870921]],[logseq____"^15logseq____",[131,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[131,logseq____"^Vlogseq____",155,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[131,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[131,logseq____"^;logseq____",logseq____"~u6535b15c-87ff-4501-b39d-089f0d39717alogseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Qlogseq____",logseq____"$\\\\text{Punkt}(a,0)$\\n\\\\begin{align}\\nl_1logseq____&=a+e\\\\\\\\\\nl_2logseq____&=a-e\\\\\\\\\\nllogseq____&=2a,\\\\quad a=\\\\frac l2\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[132,logseq____"^Flogseq____",143,536870921]],[logseq____"^15logseq____",[132,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[132,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[132,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[132,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[132,logseq____"^;logseq____",logseq____"~u6535b15c-9135-4e7c-885a-0b7379757ca1logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\text{Ellipse}logseq____&=\\\\left\\\\{(x,y)\\\\middle|\\\\frac{x^2}{a^2}+\\\\frac{y^2}{b^2}=1\\\\right\\\\}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[133,logseq____"^Flogseq____",169,536870921]],[logseq____"^15logseq____",[133,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[133,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[133,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[133,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[133,logseq____"^;logseq____",logseq____"~u6535b15c-f9fb-47de-915a-5cb7c3050eealogseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Qlogseq____",logseq____"### [[Betragsungleichungen]]logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[134,logseq____"^Flogseq____",141,536870921]],[logseq____"^15logseq____",[134,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[134,logseq____"^Vlogseq____",170,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[134,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[134,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[134,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[134,logseq____"^Hlogseq____",124,536870921]],[logseq____"^15logseq____",[134,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[134,logseq____"^;logseq____",logseq____"~u6535b15c-c8e7-4351-bfa7-f82f13d6f84flogseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nLlogseq____&=L_1\\\\cup L_2\\\\cup L_3=\\\\left(-\\\\infty,\\\\frac13\\\\right)\\\\cup\\\\left(11,\\\\infty\\\\right)\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[135,logseq____"^Flogseq____",156,536870921]],[logseq____"^15logseq____",[135,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[135,logseq____"^Vlogseq____",149,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[135,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[135,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[135,logseq____"^;logseq____",logseq____"~u6535b15c-ca56-4dc1-955d-48b29c99998alogseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Qlogseq____",logseq____"## [[Ellipse]]logseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[136,logseq____"^Flogseq____",166,536870921]],[logseq____"^15logseq____",[136,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[136,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[136,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[136,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870921]],[logseq____"^15logseq____",[136,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[136,logseq____"^Hlogseq____",111,536870921]],[logseq____"^15logseq____",[136,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[136,logseq____"^;logseq____",logseq____"~u6535b15c-e573-4259-860e-6a8689d6549clogseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Qlogseq____",logseq____"**oder** $\\\\rightarrow$ 5 ist abstand von x zu -3logseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[137,logseq____"^Flogseq____",176,536870921]],[logseq____"^15logseq____",[137,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[137,logseq____"^Vlogseq____",147,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[137,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[137,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[137,logseq____"^;logseq____",logseq____"~u6535b15c-6ebc-4915-8db8-6ab0ff25c865logseq____",536870921]],[logseq____"^15logseq____",[138,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[138,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[138,logseq____"^Flogseq____",137,536870921]],[logseq____"^15logseq____",[138,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[138,logseq____"^Vlogseq____",137,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[138,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[138,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[138,logseq____"^;logseq____",logseq____"~u6535b15c-e81e-4ab6-aa23-73b1e6a1927flogseq____",536870921]],[logseq____"^15logseq____",[139,logseq____"^Qlogseq____",logseq____"Der [[Betrag]] ist der zu [[Abstand]] 0\\n\\\\begin{align}\\nf(x)=logseq____&|x|:=logseq____&\\\\begin{cases}\\nxlogseq____&x\\\\ge0\\\\\\\\\\n-xlogseq____&xlogseq____<0\\n\\\\end{cases}\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[139,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[139,logseq____"^Flogseq____",170,536870921]],[logseq____"^15logseq____",[139,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[139,logseq____"^Vlogseq____",170,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",118,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[139,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[139,logseq____"^Hlogseq____",118,536870921]],[logseq____"^15logseq____",[139,logseq____"^Hlogseq____",121,536870921]],[logseq____"^15logseq____",[139,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[139,logseq____"^;logseq____",logseq____"~u6535b15c-8eaf-4235-b210-b5794571ccc1logseq____",536870921]],[logseq____"^15logseq____",[140,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[140,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[140,logseq____"^Flogseq____",174,536870921]],[logseq____"^15logseq____",[140,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[140,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[140,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[140,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[140,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[140,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[140,logseq____"^;logseq____",logseq____"~u6535b15c-527e-4320-b771-0689b22e304elogseq____",536870921]],[logseq____"^15logseq____",[141,logseq____"^Qlogseq____",logseq____"[[Beispiele]]\\n\\\\begin{align}\\n|5|=logseq____&5\\\\\\\\\\n|-3,3|logseq____&=3,3\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[141,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[141,logseq____"^Flogseq____",139,536870921]],[logseq____"^15logseq____",[141,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[141,logseq____"^Vlogseq____",170,536870921]],[logseq____"^15logseq____",[141,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[141,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[141,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[141,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[141,logseq____"^Hlogseq____",36,536870921]],[logseq____"^15logseq____",[141,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[141,logseq____"^;logseq____",logseq____"~u6535b15c-69a4-412d-ac4a-ffa9f0bc3e07logseq____",536870921]],[logseq____"^15logseq____",[142,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[142,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[142,logseq____"^Flogseq____",160,536870921]],[logseq____"^15logseq____",[142,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[142,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[142,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[142,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[142,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[142,logseq____"^;logseq____",logseq____"~u6535b15c-a748-48b3-872f-7d6fbefa7349logseq____",536870921]],[logseq____"^15logseq____",[143,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nelogseq____&=\\\\text{Exzentrizität}\\\\\\\\\\nl_1 + l_2 logseq____&= l\\\\\\\\\\nllogseq____&=2\\\\sqrt{a^2+e^2}\\\\\\\\\\n\\\\frac{l^2}4logseq____&=b^2+e^2\\\\\\\\\\nb^2logseq____&=\\\\frac{l^2}4-e^2\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[143,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[143,logseq____"^Flogseq____",140,536870921]],[logseq____"^15logseq____",[143,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[143,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[143,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[143,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[143,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[143,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[143,logseq____"^;logseq____",logseq____"~u6535b15c-23a9-4367-84b8-ef8b6b972de8logseq____",536870921]],[logseq____"^15logseq____",[144,logseq____"^Qlogseq____",logseq____"$(x_M,y_M)$ haben\\n\\\\begin{align}\\n\\\\underbrace{r=\\\\sqrt{(x-x_M)^2+(y-y_M)^2}}_\\\\text{Pythagoras: Abstand zwischen 2 Punkten}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[144,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[144,logseq____"^Flogseq____",159,536870921]],[logseq____"^15logseq____",[144,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[144,logseq____"^Vlogseq____",166,536870921]],[logseq____"^15logseq____",[144,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[144,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[144,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[144,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[144,logseq____"^;logseq____",logseq____"~u6535b15c-e064-4bea-b4e6-eae894e92a47logseq____",536870921]],[logseq____"^15logseq____",[145,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2a}\\\\quad x\\\\ge-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{\\\\ge0}logseq____&=x+2\\\\\\\\\\n-x+3logseq____&\\\\le x+2 logseq____&|logseq____& -2\\\\\\\\\\n-x+1logseq____&\\\\le x logseq____&|logseq____& +x\\\\\\\\\\n\\\\frac12logseq____&\\\\le x logseq____&|logseq____& :2\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____<3,x\\\\ge-2,x\\\\ge\\\\frac12\\\\right\\\\}=\\\\left[\\\\frac12,3\\\\right)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[145,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[145,logseq____"^Flogseq____",152,536870921]],[logseq____"^15logseq____",[145,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[145,logseq____"^Vlogseq____",172,536870921]],[logseq____"^15logseq____",[145,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[145,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[145,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[145,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[145,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[145,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[145,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[145,logseq____"^;logseq____",logseq____"~u6535b15c-44e7-45e0-8b61-64d0d84aa6ddlogseq____",536870921]],[logseq____"^15logseq____",[146,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&=x-3\\\\\\\\\\nx-3\\\\le|x+2|\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[146,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[146,logseq____"^Flogseq____",172,536870921]],[logseq____"^15logseq____",[146,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[146,logseq____"^Vlogseq____",172,536870921]],[logseq____"^15logseq____",[146,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[146,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[146,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[146,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[146,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[146,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[146,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[146,logseq____"^;logseq____",logseq____"~u6535b15c-88d2-4db5-8dd9-a95680c34827logseq____",536870921]],[logseq____"^15logseq____",[147,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nLlogseq____&=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big||x-3|logseq____<5\\\\right\\\\}=(-2,8)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[147,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[147,logseq____"^Flogseq____",175,536870921]],[logseq____"^15logseq____",[147,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[147,logseq____"^Vlogseq____",157,536870921]],[logseq____"^15logseq____",[147,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[147,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[147,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[147,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[147,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[147,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[147,logseq____"^;logseq____",logseq____"~u6535b15c-182c-4471-8360-51d34d4a0829logseq____",536870921]],[logseq____"^15logseq____",[148,logseq____"^Qlogseq____",logseq____"### [[Beispiele]]logseq____",536870921]],[logseq____"^15logseq____",[148,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[148,logseq____"^Flogseq____",155,536870921]],[logseq____"^15logseq____",[148,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[148,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[148,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[148,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[148,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[148,logseq____"^Hlogseq____",36,536870921]],[logseq____"^15logseq____",[148,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[148,logseq____"^;logseq____",logseq____"~u6535b15c-d491-4ca0-9f74-460b82218a7clogseq____",536870921]],[logseq____"^15logseq____",[149,logseq____"^Qlogseq____",logseq____"### Lösung mit [[Fallunterscheidung]]logseq____",536870921]],[logseq____"^15logseq____",[149,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[149,logseq____"^Flogseq____",175,536870921]],[logseq____"^15logseq____",[149,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[149,logseq____"^Vlogseq____",175,536870921]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[149,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[149,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[149,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[149,logseq____"^Hlogseq____",110,536870921]],[logseq____"^15logseq____",[149,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[149,logseq____"^;logseq____",logseq____"~u6535b15c-7cf4-4583-90e4-bb52c362d84blogseq____",536870921]],[logseq____"^15logseq____",[150,logseq____"^Qlogseq____",logseq____"Menge aller reellen Zahlen zwischen 1 und 4 inklusive 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1\\\\le x\\\\le4\\\\right\\\\}=:\\\\underbrace{[-1,4]}_\\\\text{Abgeschlossenes Interval}\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[150,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[150,logseq____"^Flogseq____",148,536870921]],[logseq____"^15logseq____",[150,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[150,logseq____"^Vlogseq____",148,536870921]],[logseq____"^15logseq____",[150,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[150,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[150,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[150,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[150,logseq____"^;logseq____",logseq____"~u6535b15c-021b-4ac3-92c7-f218896cd6c6logseq____",536870921]],[logseq____"^15logseq____",[151,logseq____"^Qlogseq____",logseq____"Regeln bei [[Ungleichungen]] sind Anwendbar aberlogseq____",536870921]],[logseq____"^15logseq____",[151,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[151,logseq____"^Flogseq____",134,536870921]],[logseq____"^15logseq____",[151,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[151,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[151,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[151,logseq____"^Hlogseq____",114,536870921]],[logseq____"^15logseq____",[151,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[151,logseq____"^;logseq____",logseq____"~u6535b15c-91b1-467a-b5e4-f45365825c04logseq____",536870921]],[logseq____"^15logseq____",[152,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2}\\\\quad xlogseq____<3$\\n\\\\begin{align}\\n|\\\\underbrace{x-3}_{logseq____<0}|logseq____&=6(x-3)=-x+3\\\\\\\\\\n-x+3logseq____&\\\\le|x+2|\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[152,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[152,logseq____"^Flogseq____",163,536870921]],[logseq____"^15logseq____",[152,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[152,logseq____"^Vlogseq____",172,536870921]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[152,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[152,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[152,logseq____"^;logseq____",logseq____"~u6535b15c-7376-4d5b-894b-2dc81286faablogseq____",536870921]],[logseq____"^15logseq____",[153,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&=-x+3\\\\\\\\\\nx-3logseq____&logseq____<5 logseq____&|logseq____&+3\\\\\\\\\\nxlogseq____&logseq____<8\\\\\\\\\\nL_2logseq____&=[3,8)\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[153,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[153,logseq____"^Flogseq____",185,536870921]],[logseq____"^15logseq____",[153,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[153,logseq____"^Vlogseq____",176,536870921]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[153,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[153,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[153,logseq____"^;logseq____",logseq____"~u6535b15c-94a8-4c29-9057-396253b7a8dflogseq____",536870921]],[logseq____"^15logseq____",[154,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2}\\\\quad -5\\\\le xlogseq____<3$\\n\\\\begin{align}\\nx+5logseq____&\\\\le0\\\\\\\\\\n|x+5|logseq____&=x+5\\\\\\\\\\nx-3logseq____&logseq____<0\\\\\\\\\\n|x-3|logseq____&=-(x-3)=-x+3\\\\\\\\\\nx+5logseq____&logseq____<2(-x+3)\\\\\\\\\\nx+5logseq____&logseq____<-2x+6 logseq____&|logseq____&+2x\\\\\\\\\\n3xlogseq____&logseq____<1 logseq____&|logseq____& :3\\\\\\\\\\nxlogseq____&logseq____<\\\\frac13\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-5\\\\le xlogseq____<3,xlogseq____<\\\\frac13\\\\right\\\\}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[154,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[154,logseq____"^Flogseq____",181,536870921]],[logseq____"^15logseq____",[154,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[154,logseq____"^Vlogseq____",149,536870921]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[154,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[154,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[154,logseq____"^;logseq____",logseq____"~u6535b15c-7489-4026-8e21-ddb1a6be809dlogseq____",536870921]],[logseq____"^15logseq____",[155,logseq____"^Qlogseq____",logseq____"## [[Lösungsmengen]]logseq____",536870921]],[logseq____"^15logseq____",[155,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[155,logseq____"^Flogseq____",177,536870921]],[logseq____"^15logseq____",[155,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[155,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[155,logseq____"^Ulogseq____",117,536870921]],[logseq____"^15logseq____",[155,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[155,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[155,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870921]],[logseq____"^15logseq____",[155,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[155,logseq____"^Hlogseq____",117,536870921]],[logseq____"^15logseq____",[155,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[155,logseq____"^;logseq____",logseq____"~u6535b15c-ef40-4418-a0e2-a18349768352logseq____",536870921]],[logseq____"^15logseq____",[156,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 3}\\\\quad xlogseq____>3$\\n\\\\begin{align}\\nx+5logseq____&logseq____>0\\\\\\\\\\n|x+5|logseq____&=x+5\\\\\\\\\\nx-3logseq____&\\\\ge0\\\\\\\\\\n|x-3|logseq____&=x-3\\\\\\\\\\nx+5logseq____&logseq____<2(x-3)\\\\\\\\\\nx+5logseq____&logseq____<2x-3 logseq____&|logseq____& -2x-5\\\\\\\\\\n-xlogseq____&logseq____<-11 logseq____&|logseq____& *(-1)\\\\\\\\\\nxlogseq____&logseq____>11\\n\\\\end{align}\\n\\\\begin{align}\\nL_3=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____>3,xlogseq____>11\\\\right\\\\}=(11,\\\\infty)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[156,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[156,logseq____"^Flogseq____",154,536870921]],[logseq____"^15logseq____",[156,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[156,logseq____"^Vlogseq____",149,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[156,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[156,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[156,logseq____"^;logseq____",logseq____"~u6535b15c-1bf9-42d2-8355-5b61bf9eddbdlogseq____",536870921]],[logseq____"^15logseq____",[157,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870921]],[logseq____"^15logseq____",[157,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[157,logseq____"^Flogseq____",151,536870921]],[logseq____"^15logseq____",[157,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[157,logseq____"^Vlogseq____",134,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[157,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[157,logseq____"^Hlogseq____",36,536870921]],[logseq____"^15logseq____",[157,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[157,logseq____"^;logseq____",logseq____"~u6535b15c-6858-49cd-af0c-1695a646820clogseq____",536870921]],[logseq____"^15logseq____",[158,logseq____"^Qlogseq____",logseq____"Bei Multiplikation oder Division mit einem Betrag einer negativen Zahl nicht Anwendbar, da ein [[Betrag]] immer Positiv istlogseq____",536870921]],[logseq____"^15logseq____",[158,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[158,logseq____"^Flogseq____",151,536870921]],[logseq____"^15logseq____",[158,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[158,logseq____"^Vlogseq____",151,536870921]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",114,536870921]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[158,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[158,logseq____"^Hlogseq____",121,536870921]],[logseq____"^15logseq____",[158,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[158,logseq____"^;logseq____",logseq____"~u6535b15c-2841-452f-8e5d-062e1163a953logseq____",536870921]],[logseq____"^15logseq____",[159,logseq____"^Qlogseq____",logseq____"[Menge]([[Mengen]]) von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]]) die den gleichen [[Abstand]] r ([[Radius]]) zu einem [festen Punkt]([[Fester Punkt]]) ([[Mittelpunkt]])logseq____",536870921]],[logseq____"^15logseq____",[159,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[159,logseq____"^Flogseq____",166,536870921]],[logseq____"^15logseq____",[159,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[159,logseq____"^Vlogseq____",166,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",108,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",109,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",112,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",118,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",125,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",126,536870921]],[logseq____"^15logseq____",[159,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",108,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",109,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",112,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",118,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",125,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",126,536870921]],[logseq____"^15logseq____",[159,logseq____"^Hlogseq____",127,536870921]],[logseq____"^15logseq____",[159,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[159,logseq____"^;logseq____",logseq____"~u6535b15c-aa5c-48e0-af38-8c35d17a461dlogseq____",536870921]],[logseq____"^15logseq____",[160,logseq____"^Qlogseq____",logseq____"wie [[Ellipse]] nur statt [[Summe]] [[Differenz]]logseq____",536870921]],[logseq____"^15logseq____",[160,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[160,logseq____"^Flogseq____",178,536870921]],[logseq____"^15logseq____",[160,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[160,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",120,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",123,536870921]],[logseq____"^15logseq____",[160,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[160,logseq____"^Hlogseq____",111,536870921]],[logseq____"^15logseq____",[160,logseq____"^Hlogseq____",120,536870921]],[logseq____"^15logseq____",[160,logseq____"^Hlogseq____",123,536870921]],[logseq____"^15logseq____",[160,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[160,logseq____"^;logseq____",logseq____"~u6535b15c-efff-4881-a8d3-a9cfccc59813logseq____",536870921]],[logseq____"^15logseq____",[161,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup L_2=(-2,8)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[161,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[161,logseq____"^Flogseq____",153,536870921]],[logseq____"^15logseq____",[161,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[161,logseq____"^Vlogseq____",176,536870921]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[161,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[161,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[161,logseq____"^;logseq____",logseq____"~u6535b15c-709e-4e33-89e0-fde88ae934bdlogseq____",536870921]],[logseq____"^15logseq____",[162,logseq____"^Qlogseq____",logseq____"# [[Mengen]]logseq____",536870921]],[logseq____"^15logseq____",[162,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[162,logseq____"^Flogseq____",122,536870921]],[logseq____"^15logseq____",[162,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[162,logseq____"^Vlogseq____",122,536870921]],[logseq____"^15logseq____",[162,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[162,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[162,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870921]],[logseq____"^15logseq____",[162,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[162,logseq____"^Hlogseq____",127,536870921]],[logseq____"^15logseq____",[162,logseq____"^17logseq____",false,536870921]],[logseq____"^15logseq____",[162,logseq____"^;logseq____",logseq____"~u6535b15c-b252-477d-ab08-6b8d8a7b03e7logseq____",536870921]],[logseq____"^15logseq____",[163,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1b}\\\\quad xlogseq____<-2\\\\quad\\\\text{Wiederspricht Bedingung}\\\\quad x\\\\ge3$logseq____",536870921]],[logseq____"^15logseq____",[163,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[163,logseq____"^Flogseq____",130,536870921]],[logseq____"^15logseq____",[163,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[163,logseq____"^Vlogseq____",172,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[163,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[163,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[163,logseq____"^;logseq____",logseq____"~u6535b15c-19ff-4d74-98dc-7ae83f4703a7logseq____",536870921]],[logseq____"^15logseq____",[164,logseq____"^Qlogseq____",logseq____"[Menge]([[Mengen]]) an [Punkten]([[Punkte]]) $(x,y)$ der [Ebene]([[Ebenen]]) bei denen die [[Summe]] der [Abstände]([[Abstand]]) der Punkte zu zwei [festen Punkten]([[Fester Punkt]]) $F_1,F_2$ ([Brennpunkte]([[Brennpunkt]])) [[konstant]] istlogseq____",536870921]],[logseq____"^15logseq____",[164,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[164,logseq____"^Flogseq____",136,536870921]],[logseq____"^15logseq____",[164,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[164,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",108,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",113,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",115,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",118,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",120,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",125,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",126,536870921]],[logseq____"^15logseq____",[164,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",108,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",113,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",115,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",118,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",120,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",125,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",126,536870921]],[logseq____"^15logseq____",[164,logseq____"^Hlogseq____",127,536870921]],[logseq____"^15logseq____",[164,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[164,logseq____"^;logseq____",logseq____"~u6535b15c-0f4d-4aca-a0c0-b2f83851b4e0logseq____",536870921]],[logseq____"^15logseq____",[165,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nM=\\\\left\\\\{\\\\underbrace{(x,y)}_\\\\text{Punkte der Ebene}\\\\in\\\\Reals^2\\\\middle|y=|x|\\\\right\\\\}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[165,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[165,logseq____"^Flogseq____",179,536870921]],[logseq____"^15logseq____",[165,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[165,logseq____"^Vlogseq____",179,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[165,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[165,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[165,logseq____"^;logseq____",logseq____"~u6535b15c-cec1-429a-86e6-2ed575dbfbbclogseq____",536870921]],[logseq____"^15logseq____",[166,logseq____"^Qlogseq____",logseq____"## [[Kreis]]logseq____",536870921]],[logseq____"^15logseq____",[166,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[166,logseq____"^Flogseq____",170,536870921]],[logseq____"^15logseq____",[166,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[166,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[166,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[166,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870921]],[logseq____"^15logseq____",[166,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[166,logseq____"^Hlogseq____",107,536870921]],[logseq____"^15logseq____",[166,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[166,logseq____"^;logseq____",logseq____"~u6535b15c-a666-497e-a27b-a5eb5dae6648logseq____",536870921]],[logseq____"^15logseq____",[167,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup L_2=[3,\\\\infty)\\\\cup\\\\left[\\\\frac12,3\\\\right)=\\\\left[\\\\frac12,\\\\infty\\\\right)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[167,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[167,logseq____"^Flogseq____",183,536870921]],[logseq____"^15logseq____",[167,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[167,logseq____"^Vlogseq____",172,536870921]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[167,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[167,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[167,logseq____"^;logseq____",logseq____"~u6535b15c-bd4e-479f-bc93-1192a8b881belogseq____",536870921]],[logseq____"^15logseq____",[168,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\frac{x^2}{a^2}-\\\\frac{y^2}{b^2}logseq____&=1\\\\\\\\\\n\\\\text{Hyperbel}logseq____&=\\\\left\\\\{(x,y)\\\\middle|\\\\frac{x^2}{a^2}-\\\\frac{y^2}{b^2}=1\\\\right\\\\}\\\\\\\\\\ny^2logseq____&=\\\\frac{b^2}{a^2}x^2-b^2\\\\\\\\\\ny^2logseq____&=\\\\frac{b^2}{a^2}\\\\left(x^2-\\\\frac1{a^2}\\\\right)\\\\\\\\\\nylogseq____&=\\\\pm\\\\frac ba \\\\sqrt{x^2-\\\\frac1{a^2}}\\\\\\\\\\nylogseq____&=\\\\pm\\\\frac ba |x| \\\\underbrace{\\\\sqrt{1-\\\\frac1{a^2x^2}}}_{\\\\rightarrow 1}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[168,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[168,logseq____"^Flogseq____",142,536870921]],[logseq____"^15logseq____",[168,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[168,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[168,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[168,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[168,logseq____"^;logseq____",logseq____"~u6535b15c-3072-49ed-bd8f-6707891d84d0logseq____",536870921]],[logseq____"^15logseq____",[169,logseq____"^Qlogseq____",logseq____"$\\\\text{Punkt(0,b)}$\\n\\\\begin{align}\\nl_1logseq____&=\\\\sqrt{b^2+e^2}=a\\\\\\\\\\nl_1^2logseq____&=b^2+e^2\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[169,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[169,logseq____"^Flogseq____",132,536870921]],[logseq____"^15logseq____",[169,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[169,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[169,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[169,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[169,logseq____"^;logseq____",logseq____"~u6535b15c-79cf-4146-ac62-d5508e5cf02alogseq____",536870921]],[logseq____"^15logseq____",[170,logseq____"^Qlogseq____",logseq____"## [[Betrag]]logseq____",536870921]],[logseq____"^15logseq____",[170,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[170,logseq____"^Flogseq____",148,536870921]],[logseq____"^15logseq____",[170,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[170,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[170,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[170,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870921]],[logseq____"^15logseq____",[170,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[170,logseq____"^Hlogseq____",121,536870921]],[logseq____"^15logseq____",[170,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[170,logseq____"^;logseq____",logseq____"~u6535b15c-37c9-4920-8ff1-226adebc7779logseq____",536870921]],[logseq____"^15logseq____",[171,logseq____"^Qlogseq____",logseq____"$y=\\\\frac ba x, y=-\\\\frac ba x$ sind [Asymptoten]([[Asymptote]]) der [[Hyperbel]]logseq____",536870921]],[logseq____"^15logseq____",[171,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[171,logseq____"^Flogseq____",168,536870921]],[logseq____"^15logseq____",[171,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[171,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",116,536870921]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[171,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[171,logseq____"^Hlogseq____",116,536870921]],[logseq____"^15logseq____",[171,logseq____"^Hlogseq____",119,536870921]],[logseq____"^15logseq____",[171,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[171,logseq____"^;logseq____",logseq____"~u6535b15c-6547-44e8-b757-1be8de406f24logseq____",536870921]],[logseq____"^15logseq____",[172,logseq____"^Qlogseq____",logseq____"### Lösung mit [[Fallunterscheidung]]logseq____",536870921]],[logseq____"^15logseq____",[172,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[172,logseq____"^Flogseq____",180,536870921]],[logseq____"^15logseq____",[172,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[172,logseq____"^Vlogseq____",180,536870921]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[172,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[172,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[172,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[172,logseq____"^Hlogseq____",110,536870921]],[logseq____"^15logseq____",[172,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[172,logseq____"^;logseq____",logseq____"~u6535b15c-f5ed-4abd-b6ae-85ac00fa0b91logseq____",536870921]],[logseq____"^15logseq____",[173,logseq____"^Qlogseq____",logseq____"Menge aller rellen Zahlen zwischen 4 und $\\\\infty$ ohne 4 und $\\\\infty$\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____>4\\\\right\\\\}=:(4,\\\\infty)\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[173,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[173,logseq____"^Flogseq____",182,536870921]],[logseq____"^15logseq____",[173,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[173,logseq____"^Vlogseq____",148,536870921]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[173,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[173,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[173,logseq____"^;logseq____",logseq____"~u6535b15c-ed59-4be8-a8bb-5180a8edaee4logseq____",536870921]],[logseq____"^15logseq____",[174,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[174,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[174,logseq____"^Flogseq____",164,536870921]],[logseq____"^15logseq____",[174,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[174,logseq____"^Vlogseq____",136,536870921]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",111,536870921]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[174,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[174,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[174,logseq____"^;logseq____",logseq____"~u6535b15c-041c-4864-8360-61f331baf366logseq____",536870921]],[logseq____"^15logseq____",[175,logseq____"^Qlogseq____",logseq____"\\\\begin{gather}\\n\\\\frac{|x+5|}{|x-3|}logseq____<2\\\\quad\\\\Bigm|*|x-3|\\\\qquad x\\\\ne3\\\\\\\\\\nL=\\\\left\\\\{ x\\\\in \\\\Reals \\\\Big| |x+5|logseq____<2|x-3|\\\\right\\\\}\\\\\\\\\\n\\\\end{gather}logseq____",536870921]],[logseq____"^15logseq____",[175,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[175,logseq____"^Flogseq____",180,536870921]],[logseq____"^15logseq____",[175,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[175,logseq____"^Vlogseq____",157,536870921]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[175,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[175,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[175,logseq____"^;logseq____",logseq____"~u6535b15c-210b-48b5-8937-906e69fb6964logseq____",536870921]],[logseq____"^15logseq____",[176,logseq____"^Qlogseq____",logseq____"### Lösung mit [[Fallunterscheidung]]logseq____",536870921]],[logseq____"^15logseq____",[176,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[176,logseq____"^Flogseq____",147,536870921]],[logseq____"^15logseq____",[176,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[176,logseq____"^Vlogseq____",147,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[176,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[176,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870921]],[logseq____"^15logseq____",[176,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[176,logseq____"^Hlogseq____",110,536870921]],[logseq____"^15logseq____",[176,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[176,logseq____"^;logseq____",logseq____"~u6535b15c-7785-4e86-b170-daf0b934c72flogseq____",536870921]],[logseq____"^15logseq____",[177,logseq____"^Qlogseq____",logseq____"$\\\\{a,b,c\\\\}$logseq____",536870921]],[logseq____"^15logseq____",[177,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[177,logseq____"^Flogseq____",162,536870921]],[logseq____"^15logseq____",[177,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[177,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[177,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[177,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[177,logseq____"^;logseq____",logseq____"~u6535b15c-7326-4b18-b8cc-2157f6db20a7logseq____",536870921]],[logseq____"^15logseq____",[178,logseq____"^Qlogseq____",logseq____"## [[Hyperbel]]logseq____",536870921]],[logseq____"^15logseq____",[178,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[178,logseq____"^Flogseq____",136,536870921]],[logseq____"^15logseq____",[178,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[178,logseq____"^Vlogseq____",162,536870921]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",119,536870921]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[178,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[178,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870921]],[logseq____"^15logseq____",[178,logseq____"^Jlogseq____",[],536870921]],[logseq____"^15logseq____",[178,logseq____"^Hlogseq____",119,536870921]],[logseq____"^15logseq____",[178,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[178,logseq____"^;logseq____",logseq____"~u6535b15c-3150-470b-b052-b4671d8d811blogseq____",536870921]],[logseq____"^15logseq____",[179,logseq____"^Qlogseq____",logseq____"logseq____",536870921]],[logseq____"^15logseq____",[179,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[179,logseq____"^Flogseq____",138,536870921]],[logseq____"^15logseq____",[179,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[179,logseq____"^Vlogseq____",137,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[179,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[179,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[179,logseq____"^;logseq____",logseq____"~u6535b15c-bf8f-426b-834a-e60872a0a220logseq____",536870921]],[logseq____"^15logseq____",[180,logseq____"^Qlogseq____",logseq____"$$L=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_{0\\\\notin L}\\\\:\\\\middle|\\\\:\\\\underbrace{|x-3|\\\\le|x+2}_{1\\\\in L}\\\\right\\\\}$$\\n$0\\\\notin L\\\\rightarrow\\\\text{0 steht nicht in Lösungsmenge}$\\n$1\\\\in L\\\\rightarrow\\\\text{1 gehört zu Lösungsmenge}$logseq____",536870921]],[logseq____"^15logseq____",[180,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[180,logseq____"^Flogseq____",157,536870921]],[logseq____"^15logseq____",[180,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[180,logseq____"^Vlogseq____",157,536870921]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[180,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[180,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[180,logseq____"^;logseq____",logseq____"~u6535b15c-3eb5-4a4f-b843-23e45c4baca7logseq____",536870921]],[logseq____"^15logseq____",[181,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1} \\\\quad xlogseq____<-5$\\n\\\\begin{align}\\nx+5logseq____&logseq____<0\\\\\\\\\\n|x+5|logseq____&=-(x+5)=-x-5\\\\\\\\\\nx-3logseq____&logseq____<0\\\\\\\\\\n|x-3|logseq____&=-(x-3)=-x+3\\\\\\\\\\n-x-5logseq____&logseq____< 2(-x+3)\\\\\\\\\\n-x-5logseq____&logseq____<-2x+6 logseq____&|logseq____&+5+2x\\\\\\\\\\nxlogseq____<11\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____<-5,x\\\\le11\\\\right\\\\}=(-\\\\infty,-5)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[181,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[181,logseq____"^Flogseq____",149,536870921]],[logseq____"^15logseq____",[181,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[181,logseq____"^Vlogseq____",149,536870921]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[181,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[181,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[181,logseq____"^;logseq____",logseq____"~u6535b15c-c578-4563-a5b8-c5ba28340499logseq____",536870921]],[logseq____"^15logseq____",[182,logseq____"^Qlogseq____",logseq____"Menge aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____<xlogseq____<4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes interval}\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[182,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[182,logseq____"^Flogseq____",150,536870921]],[logseq____"^15logseq____",[182,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[182,logseq____"^Vlogseq____",148,536870921]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[182,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[182,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[182,logseq____"^;logseq____",logseq____"~u6535b15c-2de0-4fbf-ad98-41b6b51924e4logseq____",536870921]],[logseq____"^15logseq____",[183,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2b}\\\\quad xlogseq____<-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____<0}logseq____&=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&\\\\le -x-2 logseq____&|logseq____&+x\\\\\\\\\\n3logseq____&\\\\le-2logseq____&logseq____&\\\\underset{falsche Aussage}{f.A}\\\\\\\\\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[183,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[183,logseq____"^Flogseq____",145,536870921]],[logseq____"^15logseq____",[183,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[183,logseq____"^Vlogseq____",172,536870921]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[183,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[183,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[183,logseq____"^;logseq____",logseq____"~u6535b15c-ca51-40e3-bdfd-cb056a04b936logseq____",536870921]],[logseq____"^15logseq____",[184,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nK=\\\\left\\\\{(x,y)\\\\in \\\\Reals^2 \\\\Big| (x-x_M)^2+(y-y_M)^2=r^2\\\\right\\\\}\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[184,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[184,logseq____"^Flogseq____",129,536870921]],[logseq____"^15logseq____",[184,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[184,logseq____"^Vlogseq____",166,536870921]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",107,536870921]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[184,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[184,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[184,logseq____"^;logseq____",logseq____"~u6535b15c-2d19-4f5a-923e-01a3a66cae68logseq____",536870921]],[logseq____"^15logseq____",[185,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 1}\\\\quad xlogseq____<3$\\n\\\\begin{align}\\n|x-3|logseq____&=-x+3\\\\\\\\\\n-x+3logseq____&logseq____<5 logseq____&|logseq____&-3\\\\\\\\\\n-xlogseq____&logseq____<2 logseq____&|logseq____&*-1\\\\\\\\\\nxlogseq____&logseq____>-2\\\\\\\\\\nL_1logseq____&=(-2,3)\\n\\\\end{align}logseq____",536870921]],[logseq____"^15logseq____",[185,logseq____"^Ologseq____",logseq____"^16logseq____",536870921]],[logseq____"^15logseq____",[185,logseq____"^Flogseq____",176,536870921]],[logseq____"^15logseq____",[185,logseq____"^Xlogseq____",122,536870921]],[logseq____"^15logseq____",[185,logseq____"^Vlogseq____",176,536870921]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",36,536870921]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",110,536870921]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",121,536870921]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",122,536870921]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",124,536870921]],[logseq____"^15logseq____",[185,logseq____"^Ulogseq____",127,536870921]],[logseq____"^15logseq____",[185,logseq____"^17logseq____",true,536870921]],[logseq____"^15logseq____",[185,logseq____"^;logseq____",logseq____"~u6535b15c-e2b3-4163-9f7b-8156bae2d01flogseq____",536870921]],[logseq____"^15logseq____",[187,logseq____"^Klogseq____",1698017628766,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[187,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[187,logseq____"^Ylogseq____",logseq____"grundlagen und diskrete strukturenlogseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^11logseq____",logseq____"Grundlagen und Diskrete Strukturenlogseq____",536870922]],[logseq____"^15logseq____",[187,logseq____"^Blogseq____",1698017628766,536870922]],[logseq____"^15logseq____",[187,logseq____"^;logseq____",logseq____"~u6535b15d-0301-4b9d-80aa-cb858109655flogseq____",536870931]],[logseq____"^15logseq____",[188,logseq____"^Klogseq____",1698017628766,536870922]],[logseq____"^15logseq____",[188,logseq____"^@logseq____",false,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ylogseq____",logseq____"grundlagen und diskrete strukturen/23-10-10logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Alogseq____",187,536870922]],[logseq____"^15logseq____",[188,logseq____"^11logseq____",logseq____"Grundlagen und Diskrete Strukturen/23-10-10logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Blogseq____",1698017628766,536870922]],[logseq____"^15logseq____",[188,logseq____"^;logseq____",logseq____"~u6535b15c-61cb-4385-8658-21a17e76cb8blogseq____",536870923]],[logseq____"^15logseq____",[189,logseq____"^Qlogseq____",logseq____"[[Grundlagen und Diskrete Strukturen/23-10-10]]logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Flogseq____",187,536870922]],[logseq____"^15logseq____",[189,logseq____"^Xlogseq____",187,536870922]],[logseq____"^15logseq____",[189,logseq____"^Vlogseq____",187,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",187,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",188,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",187,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",188,536870922]],[logseq____"^15logseq____",[189,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[189,logseq____"^;logseq____",logseq____"~u6535b15c-5140-43fc-9965-7e5893aab372logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Klogseq____",1698017628885,536870923]],[logseq____"^15logseq____",[191,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[191,logseq____"^Ylogseq____",logseq____"wahrheitswerteverlauflogseq____",536870923]],[logseq____"^15logseq____",[191,logseq____"^11logseq____",logseq____"Wahrheitswerteverlauflogseq____",536870923]],[logseq____"^15logseq____",[191,logseq____"^Blogseq____",1698017628885,536870923]],[logseq____"^15logseq____",[191,logseq____"^;logseq____",logseq____"~u6535b15c-3e6b-4a98-af27-1b886e1c9526logseq____",536870923]],[logseq____"^15logseq____",[192,logseq____"^Klogseq____",1698017628875,536870923]],[logseq____"^15logseq____",[192,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[192,logseq____"^Ylogseq____",logseq____"aussagenlogische variablelogseq____",536870923]],[logseq____"^15logseq____",[192,logseq____"^11logseq____",logseq____"Aussagenlogische Variablelogseq____",536870923]],[logseq____"^15logseq____",[192,logseq____"^Blogseq____",1698017628875,536870923]],[logseq____"^15logseq____",[192,logseq____"^;logseq____",logseq____"~u6535b15c-f626-4dfe-896d-3e18eb712841logseq____",536870923]],[logseq____"^15logseq____",[193,logseq____"^Klogseq____",1698017628869,536870923]],[logseq____"^15logseq____",[193,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[193,logseq____"^Ylogseq____",logseq____"wikipedialogseq____",536870923]],[logseq____"^15logseq____",[193,logseq____"^11logseq____",logseq____"Wikipedialogseq____",536870923]],[logseq____"^15logseq____",[193,logseq____"^Blogseq____",1698017628869,536870923]],[logseq____"^15logseq____",[193,logseq____"^;logseq____",logseq____"~u6535b15c-c003-4e1e-bc2e-4e736bd764f3logseq____",536870923]],[logseq____"^15logseq____",[194,logseq____"^Klogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[194,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[194,logseq____"^Ylogseq____",logseq____"formellogseq____",536870923]],[logseq____"^15logseq____",[194,logseq____"^11logseq____",logseq____"Formellogseq____",536870923]],[logseq____"^15logseq____",[194,logseq____"^Blogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[194,logseq____"^;logseq____",logseq____"~u6535b15c-412a-48f6-93a6-ad111600a16flogseq____",536870923]],[logseq____"^15logseq____",[195,logseq____"^Klogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[195,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[195,logseq____"^Ylogseq____",logseq____"wahrheitswertlogseq____",536870923]],[logseq____"^15logseq____",[195,logseq____"^11logseq____",logseq____"Wahrheitswertlogseq____",536870923]],[logseq____"^15logseq____",[195,logseq____"^Blogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[195,logseq____"^;logseq____",logseq____"~u6535b15d-c834-4cc4-a192-ef32efad41b2logseq____",536870924]],[logseq____"^15logseq____",[196,logseq____"^Klogseq____",1698017628869,536870923]],[logseq____"^15logseq____",[196,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[196,logseq____"^Ylogseq____",logseq____"\\logseq____"mathematische grundlagen der informatik\\logseq____", 5. auflage 2011logseq____",536870923]],[logseq____"^15logseq____",[196,logseq____"^11logseq____",logseq____"\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011logseq____",536870923]],[logseq____"^15logseq____",[196,logseq____"^Blogseq____",1698017628869,536870923]],[logseq____"^15logseq____",[196,logseq____"^;logseq____",logseq____"~u6535b15c-c43b-405e-b5c8-bb80de6e52c7logseq____",536870923]],[logseq____"^15logseq____",[197,logseq____"^Klogseq____",1698017628886,536870923]],[logseq____"^15logseq____",[197,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[197,logseq____"^Ylogseq____",logseq____"tantologielogseq____",536870923]],[logseq____"^15logseq____",[197,logseq____"^11logseq____",logseq____"Tantologielogseq____",536870923]],[logseq____"^15logseq____",[197,logseq____"^Blogseq____",1698017628886,536870923]],[logseq____"^15logseq____",[197,logseq____"^;logseq____",logseq____"~u6535b15c-64d6-4bb1-af51-0ce05ab3285dlogseq____",536870923]],[logseq____"^15logseq____",[198,logseq____"^Klogseq____",1698017628882,536870923]],[logseq____"^15logseq____",[198,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[198,logseq____"^Ylogseq____",logseq____"kontradiktionlogseq____",536870923]],[logseq____"^15logseq____",[198,logseq____"^11logseq____",logseq____"Kontradiktionlogseq____",536870923]],[logseq____"^15logseq____",[198,logseq____"^Blogseq____",1698017628882,536870923]],[logseq____"^15logseq____",[198,logseq____"^;logseq____",logseq____"~u6535b15c-cfa0-468e-8f2c-40d3b25654e9logseq____",536870923]],[logseq____"^15logseq____",[199,logseq____"^Klogseq____",1698017628878,536870923]],[logseq____"^15logseq____",[199,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[199,logseq____"^Ylogseq____",logseq____"variablenlogseq____",536870923]],[logseq____"^15logseq____",[199,logseq____"^11logseq____",logseq____"Variablenlogseq____",536870923]],[logseq____"^15logseq____",[199,logseq____"^Blogseq____",1698017628878,536870923]],[logseq____"^15logseq____",[199,logseq____"^;logseq____",logseq____"~u6535b15d-be95-4319-94d3-39eb93dca419logseq____",536870924]],[logseq____"^15logseq____",[200,logseq____"^Klogseq____",1698017628873,536870923]],[logseq____"^15logseq____",[200,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[200,logseq____"^Ylogseq____",logseq____"semantiklogseq____",536870923]],[logseq____"^15logseq____",[200,logseq____"^11logseq____",logseq____"Semantiklogseq____",536870923]],[logseq____"^15logseq____",[200,logseq____"^Blogseq____",1698017628873,536870923]],[logseq____"^15logseq____",[200,logseq____"^;logseq____",logseq____"~u6535b15c-d9bf-4b5d-9a22-a0bb69bfcdeclogseq____",536870923]],[logseq____"^15logseq____",[201,logseq____"^Klogseq____",1698017628886,536870923]],[logseq____"^15logseq____",[201,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[201,logseq____"^Ylogseq____",logseq____"logisch äquivalentlogseq____",536870923]],[logseq____"^15logseq____",[201,logseq____"^11logseq____",logseq____"Logisch Äquivalentlogseq____",536870923]],[logseq____"^15logseq____",[201,logseq____"^Blogseq____",1698017628886,536870923]],[logseq____"^15logseq____",[201,logseq____"^;logseq____",logseq____"~u6535b15c-b19e-4f62-942a-69c32cca5ce0logseq____",536870923]],[logseq____"^15logseq____",[202,logseq____"^Klogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[202,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[202,logseq____"^Ylogseq____",logseq____"tabellenregelnlogseq____",536870923]],[logseq____"^15logseq____",[202,logseq____"^11logseq____",logseq____"Tabellenregelnlogseq____",536870923]],[logseq____"^15logseq____",[202,logseq____"^Blogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[202,logseq____"^;logseq____",logseq____"~u6535b15c-7ac6-4aa4-9667-26154c80077elogseq____",536870923]],[logseq____"^15logseq____",[203,logseq____"^Klogseq____",1698017628872,536870923]],[logseq____"^15logseq____",[203,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[203,logseq____"^Ylogseq____",logseq____"aussagenlogseq____",536870923]],[logseq____"^15logseq____",[203,logseq____"^11logseq____",logseq____"Aussagenlogseq____",536870923]],[logseq____"^15logseq____",[203,logseq____"^Blogseq____",1698017628872,536870923]],[logseq____"^15logseq____",[203,logseq____"^;logseq____",logseq____"~u6535b15d-32ed-47bd-bc38-07485f24bc00logseq____",536870924]],[logseq____"^15logseq____",[204,logseq____"^Klogseq____",1698017628877,536870923]],[logseq____"^15logseq____",[204,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[204,logseq____"^Ylogseq____",logseq____"verknüpfungenlogseq____",536870923]],[logseq____"^15logseq____",[204,logseq____"^11logseq____",logseq____"Verknüpfungenlogseq____",536870923]],[logseq____"^15logseq____",[204,logseq____"^Blogseq____",1698017628877,536870923]],[logseq____"^15logseq____",[204,logseq____"^;logseq____",logseq____"~u6535b15c-75d5-4c2e-8bad-97c6f56eac0flogseq____",536870923]],[logseq____"^15logseq____",[205,logseq____"^Klogseq____",1698017628878,536870923]],[logseq____"^15logseq____",[205,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[205,logseq____"^Ylogseq____",logseq____"aussageformellogseq____",536870923]],[logseq____"^15logseq____",[205,logseq____"^11logseq____",logseq____"Aussageformellogseq____",536870923]],[logseq____"^15logseq____",[205,logseq____"^Blogseq____",1698017628878,536870923]],[logseq____"^15logseq____",[205,logseq____"^;logseq____",logseq____"~u6535b15c-9325-4b3c-a973-6b6195bbe821logseq____",536870923]],[logseq____"^15logseq____",[206,logseq____"^Klogseq____",1698017628874,536870923]],[logseq____"^15logseq____",[206,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[206,logseq____"^Ylogseq____",logseq____"syntaxlogseq____",536870923]],[logseq____"^15logseq____",[206,logseq____"^11logseq____",logseq____"Syntaxlogseq____",536870923]],[logseq____"^15logseq____",[206,logseq____"^Blogseq____",1698017628874,536870923]],[logseq____"^15logseq____",[206,logseq____"^;logseq____",logseq____"~u6535b15c-80e4-4ec7-be98-a461f0e1a37flogseq____",536870923]],[logseq____"^15logseq____",[207,logseq____"^Klogseq____",1698017628871,536870923]],[logseq____"^15logseq____",[207,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[207,logseq____"^Ylogseq____",logseq____"verknüpfung von aussagenlogseq____",536870923]],[logseq____"^15logseq____",[207,logseq____"^11logseq____",logseq____"Verknüpfung von Aussagenlogseq____",536870923]],[logseq____"^15logseq____",[207,logseq____"^Blogseq____",1698017628871,536870923]],[logseq____"^15logseq____",[207,logseq____"^;logseq____",logseq____"~u6535b15c-8756-449b-9d15-a4fcdd40e76alogseq____",536870923]],[logseq____"^15logseq____",[208,logseq____"^Klogseq____",1698017628885,536870923]],[logseq____"^15logseq____",[208,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[208,logseq____"^Ylogseq____",logseq____"schreibweiselogseq____",536870923]],[logseq____"^15logseq____",[208,logseq____"^11logseq____",logseq____"Schreibweiselogseq____",536870923]],[logseq____"^15logseq____",[208,logseq____"^Blogseq____",1698017628885,536870923]],[logseq____"^15logseq____",[208,logseq____"^;logseq____",logseq____"~u6535b15c-4882-4d69-9bfc-4bed89d57791logseq____",536870923]],[logseq____"^15logseq____",[209,logseq____"^Klogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[209,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[209,logseq____"^Ylogseq____",logseq____"belegunglogseq____",536870923]],[logseq____"^15logseq____",[209,logseq____"^11logseq____",logseq____"Belegunglogseq____",536870923]],[logseq____"^15logseq____",[209,logseq____"^Blogseq____",1698017628879,536870923]],[logseq____"^15logseq____",[209,logseq____"^;logseq____",logseq____"~u6535b15c-7146-4a61-b02f-a58ffdd08b8elogseq____",536870923]],[logseq____"^15logseq____",[210,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870923]],[logseq____"^15logseq____",[210,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[210,logseq____"^Flogseq____",214,536870923]],[logseq____"^15logseq____",[210,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[210,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",191,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",201,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",208,536870923]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",191,536870923]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",201,536870923]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",208,536870923]],[logseq____"^15logseq____",[210,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[210,logseq____"^;logseq____",logseq____"~u6535b15c-dd23-4fc8-b886-37cf02c94fa9logseq____",536870923]],[logseq____"^15logseq____",[211,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870923]],[logseq____"^15logseq____",[211,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[211,logseq____"^Flogseq____",210,536870923]],[logseq____"^15logseq____",[211,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[211,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",197,536870923]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[211,logseq____"^Hlogseq____",197,536870923]],[logseq____"^15logseq____",[211,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[211,logseq____"^;logseq____",logseq____"~u6535b15c-96a7-48b7-9900-3cb16d89107alogseq____",536870923]],[logseq____"^15logseq____",[212,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____",536870923]],[logseq____"^15logseq____",[212,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[212,logseq____"^Flogseq____",217,536870923]],[logseq____"^15logseq____",[212,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[212,logseq____"^Vlogseq____",213,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",191,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[212,logseq____"^Hlogseq____",191,536870923]],[logseq____"^15logseq____",[212,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[212,logseq____"^;logseq____",logseq____"~u6535b15c-ffb5-4ab2-9211-74d7ee54c445logseq____",536870923]],[logseq____"^15logseq____",[213,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870923]],[logseq____"^15logseq____",[213,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[213,logseq____"^Flogseq____",216,536870923]],[logseq____"^15logseq____",[213,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[213,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",191,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[213,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[213,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",191,536870923]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",205,536870923]],[logseq____"^15logseq____",[213,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[213,logseq____"^;logseq____",logseq____"~u6535b15c-c1a5-4eca-b8e4-14fb7862b8a9logseq____",536870923]],[logseq____"^15logseq____",[214,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870923]],[logseq____"^15logseq____",[214,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[214,logseq____"^Flogseq____",223,536870923]],[logseq____"^15logseq____",[214,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[214,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",198,536870923]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[214,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[214,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[214,logseq____"^Hlogseq____",198,536870923]],[logseq____"^15logseq____",[214,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[214,logseq____"^;logseq____",logseq____"~u6535b15c-cf18-41bd-b8d8-4d6417d59627logseq____",536870923]],[logseq____"^15logseq____",[215,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[215,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[215,logseq____"^Flogseq____",235,536870923]],[logseq____"^15logseq____",[215,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[215,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",36,536870923]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[215,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[215,logseq____"^Hlogseq____",36,536870923]],[logseq____"^15logseq____",[215,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[215,logseq____"^;logseq____",logseq____"~u6535b15c-1c62-4ca6-82b0-4a30a697f598logseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der [[Variablen]])logseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Flogseq____",220,536870923]],[logseq____"^15logseq____",[216,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[216,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",199,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ulogseq____",209,536870923]],[logseq____"^15logseq____",[216,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[216,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[216,logseq____"^Hlogseq____",199,536870923]],[logseq____"^15logseq____",[216,logseq____"^Hlogseq____",209,536870923]],[logseq____"^15logseq____",[216,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[216,logseq____"^;logseq____",logseq____"~u6535b15c-f4f1-45ea-94a4-de2dc2575b03logseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Flogseq____",213,536870923]],[logseq____"^15logseq____",[217,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[217,logseq____"^Vlogseq____",213,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",191,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",194,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",195,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",202,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ulogseq____",209,536870923]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",194,536870923]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",195,536870923]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",202,536870923]],[logseq____"^15logseq____",[217,logseq____"^Hlogseq____",209,536870923]],[logseq____"^15logseq____",[217,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[217,logseq____"^;logseq____",logseq____"~u6535b15c-bdaa-4dd1-87b5-79b03e956b7flogseq____",536870923]],[logseq____"^15logseq____",[218,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870923]],[logseq____"^15logseq____",[218,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[218,logseq____"^Flogseq____",231,536870923]],[logseq____"^15logseq____",[218,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[218,logseq____"^Vlogseq____",229,536870923]],[logseq____"^15logseq____",[218,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[218,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[218,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[218,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870923]],[logseq____"^15logseq____",[218,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[218,logseq____"^Hlogseq____",207,536870923]],[logseq____"^15logseq____",[218,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[218,logseq____"^;logseq____",logseq____"~u6535b15c-785e-4423-9aff-d4a8955d1548logseq____",536870923]],[logseq____"^15logseq____",[219,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870923]],[logseq____"^15logseq____",[219,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[219,logseq____"^Flogseq____",223,536870923]],[logseq____"^15logseq____",[219,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[219,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ulogseq____",197,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[219,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[219,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[219,logseq____"^;logseq____",logseq____"~u6535b15c-3666-4f5f-8172-74318ff04615logseq____",536870923]],[logseq____"^15logseq____",[220,logseq____"^Qlogseq____",logseq____"### [[Aussageformel]]logseq____",536870923]],[logseq____"^15logseq____",[220,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[220,logseq____"^Flogseq____",228,536870923]],[logseq____"^15logseq____",[220,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[220,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[220,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[220,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[220,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[220,logseq____"^Hlogseq____",205,536870923]],[logseq____"^15logseq____",[220,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[220,logseq____"^;logseq____",logseq____"~u6535b15c-5390-4e0a-b30b-46a51516f485logseq____",536870923]],[logseq____"^15logseq____",[221,logseq____"^Qlogseq____",logseq____"C. Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. Auflage 2011]]logseq____",536870923]],[logseq____"^15logseq____",[221,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[221,logseq____"^Flogseq____",237,536870923]],[logseq____"^15logseq____",[221,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[221,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[221,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[221,logseq____"^Ulogseq____",196,536870923]],[logseq____"^15logseq____",[221,logseq____"^Hlogseq____",196,536870923]],[logseq____"^15logseq____",[221,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[221,logseq____"^;logseq____",logseq____"~u6535b15c-2802-4093-8b3e-df42ed2aa20alogseq____",536870923]],[logseq____"^15logseq____",[222,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870923]],[logseq____"^15logseq____",[222,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[222,logseq____"^Flogseq____",214,536870923]],[logseq____"^15logseq____",[222,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[222,logseq____"^Vlogseq____",214,536870923]],[logseq____"^15logseq____",[222,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[222,logseq____"^Ulogseq____",198,536870923]],[logseq____"^15logseq____",[222,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[222,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[222,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[222,logseq____"^;logseq____",logseq____"~u6535b15c-dc88-4afb-b08f-dc4015c2328blogseq____",536870923]],[logseq____"^15logseq____",[223,logseq____"^Qlogseq____",logseq____"### [[Tantologie]]logseq____",536870923]],[logseq____"^15logseq____",[223,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[223,logseq____"^Flogseq____",213,536870923]],[logseq____"^15logseq____",[223,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[223,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[223,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[223,logseq____"^Ulogseq____",197,536870923]],[logseq____"^15logseq____",[223,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[223,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[223,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[223,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[223,logseq____"^Hlogseq____",197,536870923]],[logseq____"^15logseq____",[223,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[223,logseq____"^;logseq____",logseq____"~u6535b15c-2cc3-4f14-b068-45847b6d0673logseq____",536870923]],[logseq____"^15logseq____",[224,logseq____"^Qlogseq____",logseq____"Weitere [[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[224,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[224,logseq____"^Flogseq____",211,536870923]],[logseq____"^15logseq____",[224,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[224,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[224,logseq____"^Ulogseq____",36,536870923]],[logseq____"^15logseq____",[224,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[224,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[224,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[224,logseq____"^Hlogseq____",36,536870923]],[logseq____"^15logseq____",[224,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[224,logseq____"^;logseq____",logseq____"~u6535b15c-8d3b-4aac-9ee8-823c2e0f141elogseq____",536870923]],[logseq____"^15logseq____",[225,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870923]],[logseq____"^15logseq____",[225,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[225,logseq____"^Flogseq____",221,536870923]],[logseq____"^15logseq____",[225,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[225,logseq____"^Vlogseq____",237,536870923]],[logseq____"^15logseq____",[225,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[225,logseq____"^Ulogseq____",193,536870923]],[logseq____"^15logseq____",[225,logseq____"^Hlogseq____",193,536870923]],[logseq____"^15logseq____",[225,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[225,logseq____"^;logseq____",logseq____"~u6535b15c-2355-4bdd-ab71-2d7e5e3d22b1logseq____",536870923]],[logseq____"^15logseq____",[226,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870923]],[logseq____"^15logseq____",[226,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[226,logseq____"^Flogseq____",220,536870923]],[logseq____"^15logseq____",[226,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[226,logseq____"^Vlogseq____",220,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",43,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",204,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[226,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[226,logseq____"^Hlogseq____",43,536870923]],[logseq____"^15logseq____",[226,logseq____"^Hlogseq____",204,536870923]],[logseq____"^15logseq____",[226,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[226,logseq____"^;logseq____",logseq____"~u6535b15c-9aee-437d-8179-6bf642cc5552logseq____",536870923]],[logseq____"^15logseq____",[227,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[227,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[227,logseq____"^Flogseq____",215,536870923]],[logseq____"^15logseq____",[227,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[227,logseq____"^Vlogseq____",215,536870923]],[logseq____"^15logseq____",[227,logseq____"^Ulogseq____",36,536870923]],[logseq____"^15logseq____",[227,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[227,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[227,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[227,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[227,logseq____"^;logseq____",logseq____"~u6535b15c-cdca-4be2-b8a9-d0301180acdalogseq____",536870923]],[logseq____"^15logseq____",[228,logseq____"^Qlogseq____",logseq____"### [[Aussagenlogische Variable]]logseq____",536870923]],[logseq____"^15logseq____",[228,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[228,logseq____"^Flogseq____",232,536870923]],[logseq____"^15logseq____",[228,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[228,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[228,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[228,logseq____"^Ulogseq____",192,536870923]],[logseq____"^15logseq____",[228,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[228,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[228,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870923]],[logseq____"^15logseq____",[228,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[228,logseq____"^Hlogseq____",192,536870923]],[logseq____"^15logseq____",[228,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[228,logseq____"^;logseq____",logseq____"~u6535b15c-03f2-42a9-bd54-f17ea7a86f17logseq____",536870923]],[logseq____"^15logseq____",[229,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870923]],[logseq____"^15logseq____",[229,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[229,logseq____"^Flogseq____",237,536870923]],[logseq____"^15logseq____",[229,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[229,logseq____"^Vlogseq____",188,536870923]],[logseq____"^15logseq____",[229,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[229,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[229,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[229,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[229,logseq____"^Hlogseq____",203,536870923]],[logseq____"^15logseq____",[229,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[229,logseq____"^;logseq____",logseq____"~u6535b15c-6202-4b73-857e-d882e33d98a6logseq____",536870923]],[logseq____"^15logseq____",[230,logseq____"^Qlogseq____",logseq____"Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____",536870923]],[logseq____"^15logseq____",[230,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[230,logseq____"^Flogseq____",229,536870923]],[logseq____"^15logseq____",[230,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[230,logseq____"^Vlogseq____",229,536870923]],[logseq____"^15logseq____",[230,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[230,logseq____"^Ulogseq____",195,536870923]],[logseq____"^15logseq____",[230,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[230,logseq____"^Hlogseq____",195,536870923]],[logseq____"^15logseq____",[230,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[230,logseq____"^;logseq____",logseq____"~u6535b15c-394e-4850-9c60-1065fa44f76dlogseq____",536870923]],[logseq____"^15logseq____",[231,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&\\logseq____"5\\\\text{ ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[231,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[231,logseq____"^Flogseq____",230,536870923]],[logseq____"^15logseq____",[231,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[231,logseq____"^Vlogseq____",229,536870923]],[logseq____"^15logseq____",[231,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[231,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[231,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[231,logseq____"^;logseq____",logseq____"~u6535b15c-881e-499a-b458-db32ec9ac3edlogseq____",536870923]],[logseq____"^15logseq____",[232,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____",536870923]],[logseq____"^15logseq____",[232,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[232,logseq____"^Flogseq____",215,536870923]],[logseq____"^15logseq____",[232,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[232,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",195,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",200,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",202,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",206,536870923]],[logseq____"^15logseq____",[232,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[232,logseq____"^Hlogseq____",195,536870923]],[logseq____"^15logseq____",[232,logseq____"^Hlogseq____",200,536870923]],[logseq____"^15logseq____",[232,logseq____"^Hlogseq____",202,536870923]],[logseq____"^15logseq____",[232,logseq____"^Hlogseq____",206,536870923]],[logseq____"^15logseq____",[232,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[232,logseq____"^;logseq____",logseq____"~u6535b15c-bc02-4b8d-9fc3-cef185076139logseq____",536870923]],[logseq____"^15logseq____",[233,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____",536870923]],[logseq____"^15logseq____",[233,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[233,logseq____"^Flogseq____",216,536870923]],[logseq____"^15logseq____",[233,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[233,logseq____"^Vlogseq____",216,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",199,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",205,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[233,logseq____"^Ulogseq____",209,536870923]],[logseq____"^15logseq____",[233,logseq____"^Hlogseq____",199,536870923]],[logseq____"^15logseq____",[233,logseq____"^Hlogseq____",205,536870923]],[logseq____"^15logseq____",[233,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[233,logseq____"^;logseq____",logseq____"~u6535b15c-ba23-43d5-8f1c-533e224b6a0blogseq____",536870923]],[logseq____"^15logseq____",[234,logseq____"^Qlogseq____",logseq____"[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____",536870923]],[logseq____"^15logseq____",[234,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[234,logseq____"^Flogseq____",228,536870923]],[logseq____"^15logseq____",[234,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[234,logseq____"^Vlogseq____",228,536870923]],[logseq____"^15logseq____",[234,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[234,logseq____"^Ulogseq____",192,536870923]],[logseq____"^15logseq____",[234,logseq____"^Ulogseq____",199,536870923]],[logseq____"^15logseq____",[234,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[234,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[234,logseq____"^Hlogseq____",199,536870923]],[logseq____"^15logseq____",[234,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[234,logseq____"^;logseq____",logseq____"~u6535b15c-6674-4fe5-b2e2-0d307794aa26logseq____",536870923]],[logseq____"^15logseq____",[235,logseq____"^Qlogseq____",logseq____"Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&\\\\quadlogseq____& (\\logseq____"\\\\text{und}\\logseq____")\\\\\\\\\\n(p\\\\lor q) logseq____&logseq____& (\\logseq____"\\\\text{oder}\\logseq____")\\\\\\\\\\n(\\\\neg p) logseq____&logseq____& (\\logseq____"\\\\text{nicht}\\logseq____")\\\\\\\\\\n(p\\\\rightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{impliziert}\\logseq____")\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{genau dann wenn}\\logseq____")\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[235,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[235,logseq____"^Flogseq____",218,536870923]],[logseq____"^15logseq____",[235,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[235,logseq____"^Vlogseq____",218,536870923]],[logseq____"^15logseq____",[235,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[235,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[235,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[235,logseq____"^Hlogseq____",203,536870923]],[logseq____"^15logseq____",[235,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[235,logseq____"^;logseq____",logseq____"~u6535b15c-bdb9-4740-bc2c-228043f5900clogseq____",536870923]],[logseq____"^15logseq____",[236,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&\\\\rightarrow q logseq____&\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[236,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[236,logseq____"^Flogseq____",224,536870923]],[logseq____"^15logseq____",[236,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[236,logseq____"^Vlogseq____",224,536870923]],[logseq____"^15logseq____",[236,logseq____"^Ulogseq____",36,536870923]],[logseq____"^15logseq____",[236,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[236,logseq____"^Ulogseq____",203,536870923]],[logseq____"^15logseq____",[236,logseq____"^Ulogseq____",207,536870923]],[logseq____"^15logseq____",[236,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[236,logseq____"^;logseq____",logseq____"~u6535b15c-786d-4832-8cd0-4cf22a344e4blogseq____",536870923]],[logseq____"^15logseq____",[237,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870923]],[logseq____"^15logseq____",[237,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[237,logseq____"^Flogseq____",188,536870923]],[logseq____"^15logseq____",[237,logseq____"^Xlogseq____",188,536870923]],[logseq____"^15logseq____",[237,logseq____"^Vlogseq____",188,536870923]],[logseq____"^15logseq____",[237,logseq____"^Ulogseq____",188,536870923]],[logseq____"^15logseq____",[237,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[237,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[237,logseq____"^17logseq____",false,536870923]],[logseq____"^15logseq____",[237,logseq____"^;logseq____",logseq____"~u6535b15c-16ae-4372-94e1-095e074efb94logseq____",536870923]],[logseq____"^15logseq____",[239,logseq____"^Klogseq____",1698017629035,536870924]],[logseq____"^15logseq____",[239,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[239,logseq____"^Ylogseq____",logseq____"regelnlogseq____",536870924]],[logseq____"^15logseq____",[239,logseq____"^11logseq____",logseq____"Regelnlogseq____",536870924]],[logseq____"^15logseq____",[239,logseq____"^Blogseq____",1698017629035,536870924]],[logseq____"^15logseq____",[239,logseq____"^;logseq____",logseq____"~u6535b15d-1af4-4530-a5fd-a921770ed752logseq____",536870924]],[logseq____"^15logseq____",[240,logseq____"^Klogseq____",1698017629022,536870924]],[logseq____"^15logseq____",[240,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[240,logseq____"^Ylogseq____",logseq____"de morgansche regelnlogseq____",536870924]],[logseq____"^15logseq____",[240,logseq____"^11logseq____",logseq____"de Morgansche Regelnlogseq____",536870924]],[logseq____"^15logseq____",[240,logseq____"^Blogseq____",1698017629022,536870924]],[logseq____"^15logseq____",[240,logseq____"^;logseq____",logseq____"~u6535b15d-a469-4a1d-8a3b-047ea9579227logseq____",536870924]],[logseq____"^15logseq____",[241,logseq____"^Klogseq____",1698017629045,536870924]],[logseq____"^15logseq____",[241,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[241,logseq____"^Ylogseq____",logseq____"q.e.d.logseq____",536870924]],[logseq____"^15logseq____",[241,logseq____"^11logseq____",logseq____"Q.E.D.logseq____",536870924]],[logseq____"^15logseq____",[241,logseq____"^Blogseq____",1698017629045,536870924]],[logseq____"^15logseq____",[241,logseq____"^;logseq____",logseq____"~u6535b15d-31fb-4116-bae1-d3df931d4f26logseq____",536870932]],[logseq____"^15logseq____",[242,logseq____"^Klogseq____",1698017629036,536870924]],[logseq____"^15logseq____",[242,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[242,logseq____"^Ylogseq____",logseq____"große de morgansche regelnlogseq____",536870924]],[logseq____"^15logseq____",[242,logseq____"^11logseq____",logseq____"Große de Morgansche Regelnlogseq____",536870924]],[logseq____"^15logseq____",[242,logseq____"^Blogseq____",1698017629036,536870924]],[logseq____"^15logseq____",[242,logseq____"^;logseq____",logseq____"~u6535b15d-3bd0-408d-bf91-ed257004302blogseq____",536870924]],[logseq____"^15logseq____",[243,logseq____"^Klogseq____",1698017629029,536870924]],[logseq____"^15logseq____",[243,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[243,logseq____"^Ylogseq____",logseq____"aussagenlogiklogseq____",536870924]],[logseq____"^15logseq____",[243,logseq____"^11logseq____",logseq____"Aussagenlogiklogseq____",536870924]],[logseq____"^15logseq____",[243,logseq____"^Blogseq____",1698017629029,536870924]],[logseq____"^15logseq____",[243,logseq____"^;logseq____",logseq____"~u6535b15d-e4a0-4893-8f64-1e3a897c8cc2logseq____",536870924]],[logseq____"^15logseq____",[244,logseq____"^Klogseq____",1698017629042,536870924]],[logseq____"^15logseq____",[244,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[244,logseq____"^Ylogseq____",logseq____"w.z.b.w.logseq____",536870924]],[logseq____"^15logseq____",[244,logseq____"^11logseq____",logseq____"w.z.b.w.logseq____",536870924]],[logseq____"^15logseq____",[244,logseq____"^Blogseq____",1698017629042,536870924]],[logseq____"^15logseq____",[244,logseq____"^;logseq____",logseq____"~u6535b15d-efff-4a94-ad21-efa19ff02c14logseq____",536870932]],[logseq____"^15logseq____",[245,logseq____"^Klogseq____",1698017629024,536870924]],[logseq____"^15logseq____",[245,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[245,logseq____"^Ylogseq____",logseq____"kommutativlogseq____",536870924]],[logseq____"^15logseq____",[245,logseq____"^11logseq____",logseq____"kommutativlogseq____",536870924]],[logseq____"^15logseq____",[245,logseq____"^Blogseq____",1698017629024,536870924]],[logseq____"^15logseq____",[245,logseq____"^;logseq____",logseq____"~u6535b15d-43b7-495b-baf0-1207be9988fclogseq____",536870924]],[logseq____"^15logseq____",[246,logseq____"^Klogseq____",1698017629040,536870924]],[logseq____"^15logseq____",[246,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[246,logseq____"^Ylogseq____",logseq____"grundlagen und diskrete strukturen/23-10-13logseq____",536870924]],[logseq____"^15logseq____",[246,logseq____"^Alogseq____",187,536870924]],[logseq____"^15logseq____",[246,logseq____"^11logseq____",logseq____"Grundlagen und Diskrete Strukturen/23-10-13logseq____",536870924]],[logseq____"^15logseq____",[246,logseq____"^Blogseq____",1698017629040,536870924]],[logseq____"^15logseq____",[246,logseq____"^;logseq____",logseq____"~u6535b15d-f50a-477d-abd7-40adf9b8cbc3logseq____",536870924]],[logseq____"^15logseq____",[247,logseq____"^Klogseq____",1698017629038,536870924]],[logseq____"^15logseq____",[247,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[247,logseq____"^Ylogseq____",logseq____"gleichartiglogseq____",536870924]],[logseq____"^15logseq____",[247,logseq____"^11logseq____",logseq____"Gleichartiglogseq____",536870924]],[logseq____"^15logseq____",[247,logseq____"^Blogseq____",1698017629038,536870924]],[logseq____"^15logseq____",[247,logseq____"^;logseq____",logseq____"~u6535b15d-445f-4545-babd-bc70b1aab828logseq____",536870924]],[logseq____"^15logseq____",[248,logseq____"^Klogseq____",1698017629023,536870924]],[logseq____"^15logseq____",[248,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[248,logseq____"^Ylogseq____",logseq____"wechselseitig distributivlogseq____",536870924]],[logseq____"^15logseq____",[248,logseq____"^11logseq____",logseq____"wechselseitig distributivlogseq____",536870924]],[logseq____"^15logseq____",[248,logseq____"^Blogseq____",1698017629023,536870924]],[logseq____"^15logseq____",[248,logseq____"^;logseq____",logseq____"~u6535b15d-22f8-4eb4-879b-db8edd1e3869logseq____",536870924]],[logseq____"^15logseq____",[249,logseq____"^Klogseq____",1698017629025,536870924]],[logseq____"^15logseq____",[249,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[249,logseq____"^Ylogseq____",logseq____"assoziativlogseq____",536870924]],[logseq____"^15logseq____",[249,logseq____"^11logseq____",logseq____"assoziativlogseq____",536870924]],[logseq____"^15logseq____",[249,logseq____"^Blogseq____",1698017629025,536870924]],[logseq____"^15logseq____",[249,logseq____"^;logseq____",logseq____"~u6535b15d-8a1c-497b-b6cf-ff1b512911f0logseq____",536870924]],[logseq____"^15logseq____",[250,logseq____"^Klogseq____",1698017629045,536870924]],[logseq____"^15logseq____",[250,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[250,logseq____"^Ylogseq____",logseq____"beweiselogseq____",536870924]],[logseq____"^15logseq____",[250,logseq____"^11logseq____",logseq____"Beweiselogseq____",536870924]],[logseq____"^15logseq____",[250,logseq____"^Blogseq____",1698017629045,536870924]],[logseq____"^15logseq____",[250,logseq____"^;logseq____",logseq____"~u6535b15d-a022-4cb4-97af-1eb37fb39e30logseq____",536870924]],[logseq____"^15logseq____",[251,logseq____"^Klogseq____",1698017629039,536870924]],[logseq____"^15logseq____",[251,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[251,logseq____"^Ylogseq____",logseq____"quantorenlogseq____",536870924]],[logseq____"^15logseq____",[251,logseq____"^11logseq____",logseq____"Quantorenlogseq____",536870924]],[logseq____"^15logseq____",[251,logseq____"^Blogseq____",1698017629039,536870924]],[logseq____"^15logseq____",[251,logseq____"^;logseq____",logseq____"~u6535b15d-35d9-4506-b253-1c230a2689cclogseq____",536870924]],[logseq____"^15logseq____",[252,logseq____"^Klogseq____",1698017629034,536870924]],[logseq____"^15logseq____",[252,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[252,logseq____"^Ylogseq____",logseq____"allquantorlogseq____",536870924]],[logseq____"^15logseq____",[252,logseq____"^11logseq____",logseq____"Allquantorlogseq____",536870924]],[logseq____"^15logseq____",[252,logseq____"^Blogseq____",1698017629034,536870924]],[logseq____"^15logseq____",[252,logseq____"^;logseq____",logseq____"~u6535b15d-8db2-4e68-ab8c-f576562942fblogseq____",536870924]],[logseq____"^15logseq____",[253,logseq____"^Klogseq____",1698017629039,536870924]],[logseq____"^15logseq____",[253,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[253,logseq____"^Ylogseq____",logseq____"permutationlogseq____",536870924]],[logseq____"^15logseq____",[253,logseq____"^11logseq____",logseq____"Permutationlogseq____",536870924]],[logseq____"^15logseq____",[253,logseq____"^Blogseq____",1698017629039,536870924]],[logseq____"^15logseq____",[253,logseq____"^;logseq____",logseq____"~u6535b15d-38ae-4144-a90d-551631274f6blogseq____",536870924]],[logseq____"^15logseq____",[254,logseq____"^Klogseq____",1698017629036,536870924]],[logseq____"^15logseq____",[254,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[254,logseq____"^Ylogseq____",logseq____"große azzoziativgesetzelogseq____",536870924]],[logseq____"^15logseq____",[254,logseq____"^11logseq____",logseq____"Große Azzoziativgesetzelogseq____",536870924]],[logseq____"^15logseq____",[254,logseq____"^Blogseq____",1698017629036,536870924]],[logseq____"^15logseq____",[254,logseq____"^;logseq____",logseq____"~u6535b15d-b48b-4663-ae8a-993dfa9a21d9logseq____",536870924]],[logseq____"^15logseq____",[255,logseq____"^Klogseq____",1698017629024,536870924]],[logseq____"^15logseq____",[255,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[255,logseq____"^Ylogseq____",logseq____"idenpotentlogseq____",536870924]],[logseq____"^15logseq____",[255,logseq____"^11logseq____",logseq____"idenpotentlogseq____",536870924]],[logseq____"^15logseq____",[255,logseq____"^Blogseq____",1698017629024,536870924]],[logseq____"^15logseq____",[255,logseq____"^;logseq____",logseq____"~u6535b15d-9605-4994-acb6-39059c5c7343logseq____",536870924]],[logseq____"^15logseq____",[256,logseq____"^Klogseq____",1698017629023,536870924]],[logseq____"^15logseq____",[256,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[256,logseq____"^Ylogseq____",logseq____"distributivlogseq____",536870924]],[logseq____"^15logseq____",[256,logseq____"^11logseq____",logseq____"distributivlogseq____",536870924]],[logseq____"^15logseq____",[256,logseq____"^Blogseq____",1698017629023,536870924]],[logseq____"^15logseq____",[256,logseq____"^;logseq____",logseq____"~u6535b15d-1039-44fc-bf59-24a7eb8e396elogseq____",536870924]],[logseq____"^15logseq____",[257,logseq____"^Klogseq____",1698017629026,536870924]],[logseq____"^15logseq____",[257,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[257,logseq____"^Ylogseq____",logseq____"aussageformlogseq____",536870924]],[logseq____"^15logseq____",[257,logseq____"^11logseq____",logseq____"Aussageformlogseq____",536870924]],[logseq____"^15logseq____",[257,logseq____"^Blogseq____",1698017629026,536870924]],[logseq____"^15logseq____",[257,logseq____"^;logseq____",logseq____"~u6535b15d-ce3e-4953-9075-a077c55f5156logseq____",536870924]],[logseq____"^15logseq____",[258,logseq____"^Klogseq____",1698017629030,536870924]],[logseq____"^15logseq____",[258,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[258,logseq____"^Ylogseq____",logseq____"existenzquantorlogseq____",536870924]],[logseq____"^15logseq____",[258,logseq____"^11logseq____",logseq____"Existenzquantorlogseq____",536870924]],[logseq____"^15logseq____",[258,logseq____"^Blogseq____",1698017629030,536870924]],[logseq____"^15logseq____",[258,logseq____"^;logseq____",logseq____"~u6535b15d-d8a9-42ed-859d-35bf82f121b6logseq____",536870924]],[logseq____"^15logseq____",[259,logseq____"^Klogseq____",1698017629035,536870924]],[logseq____"^15logseq____",[259,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[259,logseq____"^Ylogseq____",logseq____"negationsregelnlogseq____",536870924]],[logseq____"^15logseq____",[259,logseq____"^11logseq____",logseq____"Negationsregelnlogseq____",536870924]],[logseq____"^15logseq____",[259,logseq____"^Blogseq____",1698017629035,536870924]],[logseq____"^15logseq____",[259,logseq____"^;logseq____",logseq____"~u6535b15d-7cdc-4e13-b1d5-2da2969fa2a9logseq____",536870924]],[logseq____"^15logseq____",[260,logseq____"^Klogseq____",1698017629028,536870924]],[logseq____"^15logseq____",[260,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[260,logseq____"^Ylogseq____",logseq____"satzlogseq____",536870924]],[logseq____"^15logseq____",[260,logseq____"^11logseq____",logseq____"Satzlogseq____",536870924]],[logseq____"^15logseq____",[260,logseq____"^Blogseq____",1698017629028,536870924]],[logseq____"^15logseq____",[260,logseq____"^;logseq____",logseq____"~u6535b15d-d955-45f9-bdac-d899c7dafe4clogseq____",536870924]],[logseq____"^15logseq____",[261,logseq____"^Klogseq____",1698017629026,536870924]],[logseq____"^15logseq____",[261,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[261,logseq____"^Ylogseq____",logseq____"universen (logik)logseq____",536870924]],[logseq____"^15logseq____",[261,logseq____"^11logseq____",logseq____"Universen (Logik)logseq____",536870924]],[logseq____"^15logseq____",[261,logseq____"^Blogseq____",1698017629026,536870924]],[logseq____"^15logseq____",[261,logseq____"^;logseq____",logseq____"~u6535b15d-3914-47d0-b867-450047a96107logseq____",536870924]],[logseq____"^15logseq____",[262,logseq____"^Klogseq____",1698017629030,536870924]],[logseq____"^15logseq____",[262,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[262,logseq____"^Ylogseq____",logseq____"sprachenlogseq____",536870924]],[logseq____"^15logseq____",[262,logseq____"^11logseq____",logseq____"Sprachenlogseq____",536870924]],[logseq____"^15logseq____",[262,logseq____"^Blogseq____",1698017629030,536870924]],[logseq____"^15logseq____",[262,logseq____"^;logseq____",logseq____"~u6535b15d-cd82-4cc4-907e-df00869c80b0logseq____",536870924]],[logseq____"^15logseq____",[263,logseq____"^Klogseq____",1698017629027,536870924]],[logseq____"^15logseq____",[263,logseq____"^@logseq____",false,536870924]],[logseq____"^15logseq____",[263,logseq____"^Ylogseq____",logseq____"objekt (logik)logseq____",536870924]],[logseq____"^15logseq____",[263,logseq____"^11logseq____",logseq____"Objekt (Logik)logseq____",536870924]],[logseq____"^15logseq____",[263,logseq____"^Blogseq____",1698017629027,536870924]],[logseq____"^15logseq____",[263,logseq____"^;logseq____",logseq____"~u6535b15d-ff2e-4428-a8cb-05cae0d513e3logseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Qlogseq____",logseq____"Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[264,logseq____"^Flogseq____",269,536870924]],[logseq____"^15logseq____",[264,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[264,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[264,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[264,logseq____"^;logseq____",logseq____"~u6535b15d-7977-4e70-8766-49a5d94ac798logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Qlogseq____",logseq____"Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[265,logseq____"^Flogseq____",267,536870924]],[logseq____"^15logseq____",[265,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[265,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[265,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[265,logseq____"^;logseq____",logseq____"~u6535b15d-0b66-42fd-89bc-ebd9bacc29a4logseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Qlogseq____",logseq____"Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[266,logseq____"^Flogseq____",292,536870924]],[logseq____"^15logseq____",[266,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[266,logseq____"^Vlogseq____",271,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[266,logseq____"^Hlogseq____",251,536870924]],[logseq____"^15logseq____",[266,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[266,logseq____"^;logseq____",logseq____"~u6535b15c-bee6-472e-aceb-4c426102cd88logseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\logseq____"\\\\text{x ist prim}\\logseq____" \\\\quad logseq____& \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____"\\\\underbrace{x}_{x_1}logseq____<\\\\underbrace{y}_{x_2}\\logseq____"\\\\quad logseq____&\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____"\\\\text{x ist wahr}\\logseq____"\\\\quadlogseq____&\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[267,logseq____"^Flogseq____",276,536870924]],[logseq____"^15logseq____",[267,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[267,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[267,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[267,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[267,logseq____"^;logseq____",logseq____"~u6535b15d-d690-4a01-a493-b4aa00946d59logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Qlogseq____",logseq____"Wäre $y$ aus $\\\\Reals$ mit $xlogseq____<y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____<y$, Widerspruch. $\\\\blacksquare$logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[268,logseq____"^Flogseq____",300,536870924]],[logseq____"^15logseq____",[268,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[268,logseq____"^Vlogseq____",300,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[268,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[268,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[268,logseq____"^;logseq____",logseq____"~u6535b15c-c584-4520-8517-a14651f9277blogseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Qlogseq____",logseq____"Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[269,logseq____"^Flogseq____",265,536870924]],[logseq____"^15logseq____",[269,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[269,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",243,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",262,536870924]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",243,536870924]],[logseq____"^15logseq____",[269,logseq____"^Hlogseq____",262,536870924]],[logseq____"^15logseq____",[269,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[269,logseq____"^;logseq____",logseq____"~u6535b15d-6b54-449e-af1f-91e01274c997logseq____",536870924]],[logseq____"^15logseq____",[270,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[270,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[270,logseq____"^Flogseq____",272,536870924]],[logseq____"^15logseq____",[270,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[270,logseq____"^Vlogseq____",272,536870924]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[270,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[270,logseq____"^;logseq____",logseq____"~u6535b15c-41f9-4747-a1c3-139e772771d6logseq____",536870924]],[logseq____"^15logseq____",[271,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[271,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[271,logseq____"^Flogseq____",296,536870924]],[logseq____"^15logseq____",[271,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[271,logseq____"^Vlogseq____",296,536870924]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[271,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[271,logseq____"^;logseq____",logseq____"~u6535b15c-e645-4a7a-81b8-e4f53ff33241logseq____",536870924]],[logseq____"^15logseq____",[272,logseq____"^Qlogseq____",logseq____"## [[Regeln]]logseq____",536870924]],[logseq____"^15logseq____",[272,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[272,logseq____"^Flogseq____",297,536870924]],[logseq____"^15logseq____",[272,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[272,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[272,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870924]],[logseq____"^15logseq____",[272,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",239,536870924]],[logseq____"^15logseq____",[272,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[272,logseq____"^;logseq____",logseq____"~u6535b15c-ca88-4119-83f1-16dd9787d636logseq____",536870924]],[logseq____"^15logseq____",[273,logseq____"^Qlogseq____",logseq____"Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____",536870924]],[logseq____"^15logseq____",[273,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[273,logseq____"^Flogseq____",264,536870924]],[logseq____"^15logseq____",[273,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[273,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[273,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[273,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[273,logseq____"^;logseq____",logseq____"~u6535b15d-bd9b-4fba-a001-98619e38df70logseq____",536870924]],[logseq____"^15logseq____",[274,logseq____"^Qlogseq____",logseq____"see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____",536870924]],[logseq____"^15logseq____",[274,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[274,logseq____"^Flogseq____",277,536870924]],[logseq____"^15logseq____",[274,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[274,logseq____"^Vlogseq____",277,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",240,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",245,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",248,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",249,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",255,536870924]],[logseq____"^15logseq____",[274,logseq____"^Ulogseq____",256,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",240,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",245,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",248,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",249,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",255,536870924]],[logseq____"^15logseq____",[274,logseq____"^Hlogseq____",256,536870924]],[logseq____"^15logseq____",[274,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[274,logseq____"^;logseq____",logseq____"~u6535b15d-c1ba-4e61-ad89-a8974bc35429logseq____",536870924]],[logseq____"^15logseq____",[275,logseq____"^Qlogseq____",logseq____"#FIXMElogseq____",536870924]],[logseq____"^15logseq____",[275,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[275,logseq____"^Flogseq____",297,536870924]],[logseq____"^15logseq____",[275,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[275,logseq____"^Vlogseq____",297,536870924]],[logseq____"^15logseq____",[275,logseq____"^Ulogseq____",43,536870924]],[logseq____"^15logseq____",[275,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[275,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[275,logseq____"^Hlogseq____",43,536870924]],[logseq____"^15logseq____",[275,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[275,logseq____"^;logseq____",logseq____"~u6535b15c-be1f-4bb3-ae1e-5134aaa6f13flogseq____",536870924]],[logseq____"^15logseq____",[276,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870924]],[logseq____"^15logseq____",[276,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[276,logseq____"^Flogseq____",291,536870924]],[logseq____"^15logseq____",[276,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[276,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[276,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[276,logseq____"^Hlogseq____",36,536870924]],[logseq____"^15logseq____",[276,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[276,logseq____"^;logseq____",logseq____"~u6535b15d-c790-4c9f-bf3f-d8b3021c5668logseq____",536870924]],[logseq____"^15logseq____",[277,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&\\\\equiv p, \\\\quad \\\\neg logseq____&\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[277,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[277,logseq____"^Flogseq____",287,536870924]],[logseq____"^15logseq____",[277,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[277,logseq____"^Vlogseq____",246,536870924]],[logseq____"^15logseq____",[277,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[277,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[277,logseq____"^;logseq____",logseq____"~u6535b15d-ab4d-400d-bef4-39d06c82680dlogseq____",536870924]],[logseq____"^15logseq____",[278,logseq____"^Qlogseq____",logseq____"see: [[Allquantor]] [[Existenzquantor]]logseq____",536870924]],[logseq____"^15logseq____",[278,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[278,logseq____"^Flogseq____",285,536870924]],[logseq____"^15logseq____",[278,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[278,logseq____"^Vlogseq____",285,536870924]],[logseq____"^15logseq____",[278,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[278,logseq____"^Ulogseq____",252,536870924]],[logseq____"^15logseq____",[278,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[278,logseq____"^Ulogseq____",258,536870924]],[logseq____"^15logseq____",[278,logseq____"^Hlogseq____",252,536870924]],[logseq____"^15logseq____",[278,logseq____"^Hlogseq____",258,536870924]],[logseq____"^15logseq____",[278,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[278,logseq____"^;logseq____",logseq____"~u6535b15d-cacb-4cea-a00d-a53a3ba758f2logseq____",536870924]],[logseq____"^15logseq____",[279,logseq____"^Qlogseq____",logseq____"$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, logseq____",536870924]],[logseq____"^15logseq____",[279,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[279,logseq____"^Flogseq____",280,536870924]],[logseq____"^15logseq____",[279,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[279,logseq____"^Vlogseq____",280,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",241,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",244,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[279,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[279,logseq____"^Hlogseq____",241,536870924]],[logseq____"^15logseq____",[279,logseq____"^Hlogseq____",244,536870924]],[logseq____"^15logseq____",[279,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[279,logseq____"^;logseq____",logseq____"~u6535b15c-4262-4719-bb5c-0071158f747alogseq____",536870924]],[logseq____"^15logseq____",[280,logseq____"^Qlogseq____",logseq____"Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____<x+1=y$ also $xlogseq____<y$. $\\\\blacksquare$logseq____",536870924]],[logseq____"^15logseq____",[280,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[280,logseq____"^Flogseq____",299,536870924]],[logseq____"^15logseq____",[280,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[280,logseq____"^Vlogseq____",299,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[280,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[280,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[280,logseq____"^;logseq____",logseq____"~u6535b15c-5174-447d-be84-b1567e2c1c0elogseq____",536870924]],[logseq____"^15logseq____",[281,logseq____"^Qlogseq____",logseq____"see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____",536870924]],[logseq____"^15logseq____",[281,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[281,logseq____"^Flogseq____",270,536870924]],[logseq____"^15logseq____",[281,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[281,logseq____"^Vlogseq____",270,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",242,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",254,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[281,logseq____"^Ulogseq____",259,536870924]],[logseq____"^15logseq____",[281,logseq____"^Hlogseq____",242,536870924]],[logseq____"^15logseq____",[281,logseq____"^Hlogseq____",254,536870924]],[logseq____"^15logseq____",[281,logseq____"^Hlogseq____",259,536870924]],[logseq____"^15logseq____",[281,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[281,logseq____"^;logseq____",logseq____"~u6535b15c-440a-4abe-8b67-cf6e3c4980cdlogseq____",536870924]],[logseq____"^15logseq____",[282,logseq____"^Qlogseq____",logseq____"[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____",536870924]],[logseq____"^15logseq____",[282,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[282,logseq____"^Flogseq____",286,536870924]],[logseq____"^15logseq____",[282,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[282,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[282,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[282,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[282,logseq____"^Ulogseq____",261,536870924]],[logseq____"^15logseq____",[282,logseq____"^Hlogseq____",257,536870924]],[logseq____"^15logseq____",[282,logseq____"^Hlogseq____",261,536870924]],[logseq____"^15logseq____",[282,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[282,logseq____"^;logseq____",logseq____"~u6535b15d-63f9-48ec-8de5-adb7facac00alogseq____",536870924]],[logseq____"^15logseq____",[283,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870924]],[logseq____"^15logseq____",[283,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[283,logseq____"^Flogseq____",296,536870924]],[logseq____"^15logseq____",[283,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[283,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[283,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[283,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[283,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[283,logseq____"^Hlogseq____",36,536870924]],[logseq____"^15logseq____",[283,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[283,logseq____"^;logseq____",logseq____"~u6535b15c-490a-4ccd-83cc-ea75c6caa464logseq____",536870924]],[logseq____"^15logseq____",[284,logseq____"^Qlogseq____",logseq____"Nach Ersetzung von $x$ in der AF $\\logseq____"xlogseq____<y\\logseq____"$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____"17logseq____<y\\logseq____"$logseq____",536870924]],[logseq____"^15logseq____",[284,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[284,logseq____"^Flogseq____",267,536870924]],[logseq____"^15logseq____",[284,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[284,logseq____"^Vlogseq____",267,536870924]],[logseq____"^15logseq____",[284,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[284,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[284,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[284,logseq____"^;logseq____",logseq____"~u6535b15d-450a-49a9-8c18-cf812a1dfdbalogseq____",536870924]],[logseq____"^15logseq____",[285,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[285,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[285,logseq____"^Flogseq____",273,536870924]],[logseq____"^15logseq____",[285,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[285,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[285,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[285,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[285,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[285,logseq____"^;logseq____",logseq____"~u6535b15d-6d72-4cd5-b5ba-3514a1f17015logseq____",536870924]],[logseq____"^15logseq____",[286,logseq____"^Qlogseq____",logseq____"# [[Aussageform]]logseq____",536870924]],[logseq____"^15logseq____",[286,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[286,logseq____"^Flogseq____",277,536870924]],[logseq____"^15logseq____",[286,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[286,logseq____"^Vlogseq____",246,536870924]],[logseq____"^15logseq____",[286,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[286,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[286,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870924]],[logseq____"^15logseq____",[286,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[286,logseq____"^Hlogseq____",257,536870924]],[logseq____"^15logseq____",[286,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[286,logseq____"^;logseq____",logseq____"~u6535b15d-8889-4489-ad93-5efb100263ealogseq____",536870924]],[logseq____"^15logseq____",[287,logseq____"^Qlogseq____",logseq____"# [[Regeln]]logseq____",536870924]],[logseq____"^15logseq____",[287,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[287,logseq____"^Flogseq____",246,536870924]],[logseq____"^15logseq____",[287,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[287,logseq____"^Vlogseq____",246,536870924]],[logseq____"^15logseq____",[287,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[287,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[287,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870924]],[logseq____"^15logseq____",[287,logseq____"^Jlogseq____",[],536870924]],[logseq____"^15logseq____",[287,logseq____"^Hlogseq____",239,536870924]],[logseq____"^15logseq____",[287,logseq____"^17logseq____",false,536870924]],[logseq____"^15logseq____",[287,logseq____"^;logseq____",logseq____"~u6535b15d-0be5-41e6-baa3-4392875b72aalogseq____",536870924]],[logseq____"^15logseq____",[288,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870924]],[logseq____"^15logseq____",[288,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[288,logseq____"^Flogseq____",271,536870924]],[logseq____"^15logseq____",[288,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[288,logseq____"^Vlogseq____",296,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[288,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[288,logseq____"^Hlogseq____",36,536870924]],[logseq____"^15logseq____",[288,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[288,logseq____"^;logseq____",logseq____"~u6535b15c-d1c8-4dae-8a26-6027d9a26b83logseq____",536870924]],[logseq____"^15logseq____",[289,logseq____"^Qlogseq____",logseq____"$\\\\exists x:p(x)$ ist die Aussage: \\logseq____"Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____",536870924]],[logseq____"^15logseq____",[289,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[289,logseq____"^Flogseq____",285,536870924]],[logseq____"^15logseq____",[289,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[289,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[289,logseq____"^Ulogseq____",195,536870924]],[logseq____"^15logseq____",[289,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[289,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[289,logseq____"^Hlogseq____",195,536870924]],[logseq____"^15logseq____",[289,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[289,logseq____"^;logseq____",logseq____"~u6535b15d-8f46-431e-a8bc-32d16f586f5clogseq____",536870924]],[logseq____"^15logseq____",[290,logseq____"^Qlogseq____",logseq____"Betrachte $\\logseq____"xlogseq____<y\\logseq____"$ als AF über $\\\\Reals, \\\\Reals$logseq____",536870924]],[logseq____"^15logseq____",[290,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[290,logseq____"^Flogseq____",288,536870924]],[logseq____"^15logseq____",[290,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[290,logseq____"^Vlogseq____",288,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[290,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[290,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[290,logseq____"^;logseq____",logseq____"~u6535b15c-c9c2-4644-8a5b-c52184b33b4dlogseq____",536870924]],[logseq____"^15logseq____",[291,logseq____"^Qlogseq____",logseq____"[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____",536870924]],[logseq____"^15logseq____",[291,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[291,logseq____"^Flogseq____",282,536870924]],[logseq____"^15logseq____",[291,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[291,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",199,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",203,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",260,536870924]],[logseq____"^15logseq____",[291,logseq____"^Ulogseq____",263,536870924]],[logseq____"^15logseq____",[291,logseq____"^Hlogseq____",199,536870924]],[logseq____"^15logseq____",[291,logseq____"^Hlogseq____",203,536870924]],[logseq____"^15logseq____",[291,logseq____"^Hlogseq____",260,536870924]],[logseq____"^15logseq____",[291,logseq____"^Hlogseq____",263,536870924]],[logseq____"^15logseq____",[291,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[291,logseq____"^;logseq____",logseq____"~u6535b15d-7ebf-481d-becc-f864a19eb405logseq____",536870924]],[logseq____"^15logseq____",[292,logseq____"^Qlogseq____",logseq____"wobei $\\\\pi$ eine \\logseq____"[[Permutation]]\\logseq____" der Zahl $(1,2,\\\\cdots,n)$ istlogseq____",536870924]],[logseq____"^15logseq____",[292,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[292,logseq____"^Flogseq____",271,536870924]],[logseq____"^15logseq____",[292,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[292,logseq____"^Vlogseq____",271,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",253,536870924]],[logseq____"^15logseq____",[292,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[292,logseq____"^Hlogseq____",253,536870924]],[logseq____"^15logseq____",[292,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[292,logseq____"^;logseq____",logseq____"~u6535b15c-3fe9-4ce0-a476-305ff299fedclogseq____",536870924]],[logseq____"^15logseq____",[293,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[293,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[293,logseq____"^Flogseq____",283,536870924]],[logseq____"^15logseq____",[293,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[293,logseq____"^Vlogseq____",283,536870924]],[logseq____"^15logseq____",[293,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[293,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[293,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[293,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[293,logseq____"^;logseq____",logseq____"~u6535b15c-e4de-4efc-9342-fd82f5f06cd0logseq____",536870924]],[logseq____"^15logseq____",[294,logseq____"^Qlogseq____",logseq____"Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____",536870924]],[logseq____"^15logseq____",[294,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[294,logseq____"^Flogseq____",301,536870924]],[logseq____"^15logseq____",[294,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[294,logseq____"^Vlogseq____",301,536870924]],[logseq____"^15logseq____",[294,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[294,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[294,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[294,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[294,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[294,logseq____"^;logseq____",logseq____"~u6535b15c-919d-44e9-b442-cf37869a2791logseq____",536870924]],[logseq____"^15logseq____",[295,logseq____"^Qlogseq____",logseq____"Widerspruch = ↯, #logseq____",536870924]],[logseq____"^15logseq____",[295,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[295,logseq____"^Flogseq____",268,536870924]],[logseq____"^15logseq____",[295,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[295,logseq____"^Vlogseq____",268,536870924]],[logseq____"^15logseq____",[295,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[295,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[295,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[295,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[295,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[295,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[295,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[295,logseq____"^;logseq____",logseq____"~u6535b15c-14c2-49f5-90b6-fa0e27956133logseq____",536870924]],[logseq____"^15logseq____",[296,logseq____"^Qlogseq____",logseq____"[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____",536870924]],[logseq____"^15logseq____",[296,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[296,logseq____"^Flogseq____",272,536870924]],[logseq____"^15logseq____",[296,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[296,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[296,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[296,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[296,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[296,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[296,logseq____"^Hlogseq____",247,536870924]],[logseq____"^15logseq____",[296,logseq____"^Hlogseq____",251,536870924]],[logseq____"^15logseq____",[296,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[296,logseq____"^;logseq____",logseq____"~u6535b15c-aa2a-4c30-aebe-82eb310540c9logseq____",536870924]],[logseq____"^15logseq____",[297,logseq____"^Qlogseq____",logseq____"Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____",536870924]],[logseq____"^15logseq____",[297,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[297,logseq____"^Flogseq____",289,536870924]],[logseq____"^15logseq____",[297,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[297,logseq____"^Vlogseq____",286,536870924]],[logseq____"^15logseq____",[297,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[297,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[297,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[297,logseq____"^;logseq____",logseq____"~u6535b15c-7e2d-4d02-80c1-3ff2158ca4a6logseq____",536870924]],[logseq____"^15logseq____",[298,logseq____"^Qlogseq____",logseq____"$\\\\forall x:p(x)$ ist die [Aussage]([[Aussagen]]): $\\logseq____"\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____"\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____",536870924]],[logseq____"^15logseq____",[298,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[298,logseq____"^Flogseq____",265,536870924]],[logseq____"^15logseq____",[298,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[298,logseq____"^Vlogseq____",265,536870924]],[logseq____"^15logseq____",[298,logseq____"^Ulogseq____",195,536870924]],[logseq____"^15logseq____",[298,logseq____"^Ulogseq____",203,536870924]],[logseq____"^15logseq____",[298,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[298,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[298,logseq____"^Hlogseq____",195,536870924]],[logseq____"^15logseq____",[298,logseq____"^Hlogseq____",203,536870924]],[logseq____"^15logseq____",[298,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[298,logseq____"^;logseq____",logseq____"~u6535b15d-eb1f-4588-860a-51f6054bd9dflogseq____",536870924]],[logseq____"^15logseq____",[299,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870924]],[logseq____"^15logseq____",[299,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[299,logseq____"^Flogseq____",290,536870924]],[logseq____"^15logseq____",[299,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[299,logseq____"^Vlogseq____",290,536870924]],[logseq____"^15logseq____",[299,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[299,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[299,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[299,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[299,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[299,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[299,logseq____"^Hlogseq____",250,536870924]],[logseq____"^15logseq____",[299,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[299,logseq____"^;logseq____",logseq____"~u6535b15c-1fae-4842-9d5e-c339e3fa55e0logseq____",536870924]],[logseq____"^15logseq____",[300,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870924]],[logseq____"^15logseq____",[300,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[300,logseq____"^Flogseq____",299,536870924]],[logseq____"^15logseq____",[300,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[300,logseq____"^Vlogseq____",290,536870924]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",247,536870924]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",250,536870924]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",251,536870924]],[logseq____"^15logseq____",[300,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[300,logseq____"^Hlogseq____",250,536870924]],[logseq____"^15logseq____",[300,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[300,logseq____"^;logseq____",logseq____"~u6535b15c-d3af-4188-83e2-1e7ac5a8722dlogseq____",536870924]],[logseq____"^15logseq____",[301,logseq____"^Qlogseq____",logseq____"Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____",536870924]],[logseq____"^15logseq____",[301,logseq____"^Ologseq____",logseq____"^16logseq____",536870924]],[logseq____"^15logseq____",[301,logseq____"^Flogseq____",270,536870924]],[logseq____"^15logseq____",[301,logseq____"^Xlogseq____",246,536870924]],[logseq____"^15logseq____",[301,logseq____"^Vlogseq____",272,536870924]],[logseq____"^15logseq____",[301,logseq____"^Ulogseq____",36,536870924]],[logseq____"^15logseq____",[301,logseq____"^Ulogseq____",239,536870924]],[logseq____"^15logseq____",[301,logseq____"^Ulogseq____",246,536870924]],[logseq____"^15logseq____",[301,logseq____"^Ulogseq____",257,536870924]],[logseq____"^15logseq____",[301,logseq____"^Hlogseq____",36,536870924]],[logseq____"^15logseq____",[301,logseq____"^17logseq____",true,536870924]],[logseq____"^15logseq____",[301,logseq____"^;logseq____",logseq____"~u6535b15c-635a-4b04-8b78-12fff36d4beflogseq____",536870924]],[logseq____"^15logseq____",[303,logseq____"^Klogseq____",1698017629100,536870925]],[logseq____"^15logseq____",[303,logseq____"^@logseq____",false,536870925]],[logseq____"^15logseq____",[303,logseq____"^Ylogseq____",logseq____"logarithmusgesetzelogseq____",536870925]],[logseq____"^15logseq____",[303,logseq____"^11logseq____",logseq____"Logarithmusgesetzelogseq____",536870925]],[logseq____"^15logseq____",[303,logseq____"^Blogseq____",1698017629100,536870925]],[logseq____"^15logseq____",[303,logseq____"^;logseq____",logseq____"~u6535b15d-1626-4aef-8f63-092f66289932logseq____",536870925]],[logseq____"^15logseq____",[304,logseq____"^Qlogseq____",logseq____"[[Logarithmusgesetze]]logseq____",536870925]],[logseq____"^15logseq____",[304,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[304,logseq____"^Flogseq____",32,536870925]],[logseq____"^15logseq____",[304,logseq____"^Xlogseq____",32,536870925]],[logseq____"^15logseq____",[304,logseq____"^Vlogseq____",32,536870925]],[logseq____"^15logseq____",[304,logseq____"^Ulogseq____",32,536870925]],[logseq____"^15logseq____",[304,logseq____"^Ulogseq____",303,536870925]],[logseq____"^15logseq____",[304,logseq____"^Hlogseq____",303,536870925]],[logseq____"^15logseq____",[304,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[304,logseq____"^;logseq____",logseq____"~u6535b15d-65e7-4d46-afdc-d3a23f34ee30logseq____",536870925]],[logseq____"^15logseq____",[305,logseq____"^Qlogseq____",logseq____"logseq____",536870925]],[logseq____"^15logseq____",[305,logseq____"^Ologseq____",logseq____"^16logseq____",536870925]],[logseq____"^15logseq____",[305,logseq____"^Flogseq____",304,536870925]],[logseq____"^15logseq____",[305,logseq____"^Xlogseq____",32,536870925]],[logseq____"^15logseq____",[305,logseq____"^Vlogseq____",32,536870925]],[logseq____"^15logseq____",[305,logseq____"^Ulogseq____",32,536870925]],[logseq____"^15logseq____",[305,logseq____"^17logseq____",true,536870925]],[logseq____"^15logseq____",[305,logseq____"^;logseq____",logseq____"~u6535b15d-2f1c-4680-ab37-dce19932ea01logseq____",536870925]],[logseq____"^15logseq____",[318,logseq____"^Klogseq____",1698017629135,536870928]],[logseq____"^15logseq____",[318,logseq____"^@logseq____",false,536870928]],[logseq____"^15logseq____",[318,logseq____"^Ylogseq____",logseq____"programmierung und algorithmenlogseq____",536870928]],[logseq____"^15logseq____",[318,logseq____"^11logseq____",logseq____"Programmierung und Algorithmenlogseq____",536870928]],[logseq____"^15logseq____",[318,logseq____"^Blogseq____",1698017629135,536870928]],[logseq____"^15logseq____",[318,logseq____"^;logseq____",logseq____"~u6535b15d-7d16-4c4c-bbaf-420276aca9f9logseq____",536870931]],[logseq____"^15logseq____",[319,logseq____"^Qlogseq____",logseq____"# Informationenlogseq____",536870928]],[logseq____"^15logseq____",[319,logseq____"^Ologseq____",logseq____"^16logseq____",536870928]],[logseq____"^15logseq____",[319,logseq____"^Flogseq____",318,536870928]],[logseq____"^15logseq____",[319,logseq____"^Xlogseq____",318,536870928]],[logseq____"^15logseq____",[319,logseq____"^Vlogseq____",318,536870928]],[logseq____"^15logseq____",[319,logseq____"^Ulogseq____",318,536870928]],[logseq____"^15logseq____",[319,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870928]],[logseq____"^15logseq____",[319,logseq____"^Jlogseq____",[],536870928]],[logseq____"^15logseq____",[319,logseq____"^17logseq____",false,536870928]],[logseq____"^15logseq____",[319,logseq____"^;logseq____",logseq____"~u6535b15d-3f7f-43a4-8f32-180ef27870bdlogseq____",536870928]],[logseq____"^15logseq____",[320,logseq____"^Qlogseq____",logseq____"Bestehquote: 40%logseq____",536870928]],[logseq____"^15logseq____",[320,logseq____"^Ologseq____",logseq____"^16logseq____",536870928]],[logseq____"^15logseq____",[320,logseq____"^Flogseq____",319,536870928]],[logseq____"^15logseq____",[320,logseq____"^Xlogseq____",318,536870928]],[logseq____"^15logseq____",[320,logseq____"^Vlogseq____",319,536870928]],[logseq____"^15logseq____",[320,logseq____"^Ulogseq____",318,536870928]],[logseq____"^15logseq____",[320,logseq____"^17logseq____",true,536870928]],[logseq____"^15logseq____",[320,logseq____"^;logseq____",logseq____"~u6535b15d-6d47-4122-994f-c9ecd76d0c08logseq____",536870928]],[logseq____"^15logseq____",[321,logseq____"^Qlogseq____",logseq____"## Bonuspunktelogseq____",536870928]],[logseq____"^15logseq____",[321,logseq____"^Ologseq____",logseq____"^16logseq____",536870928]],[logseq____"^15logseq____",[321,logseq____"^Flogseq____",320,536870928]],[logseq____"^15logseq____",[321,logseq____"^Xlogseq____",318,536870928]],[logseq____"^15logseq____",[321,logseq____"^Vlogseq____",319,536870928]],[logseq____"^15logseq____",[321,logseq____"^Ulogseq____",318,536870928]],[logseq____"^15logseq____",[321,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870928]],[logseq____"^15logseq____",[321,logseq____"^Jlogseq____",[],536870928]],[logseq____"^15logseq____",[321,logseq____"^17logseq____",true,536870928]],[logseq____"^15logseq____",[321,logseq____"^;logseq____",logseq____"~u6535b15d-9c60-4836-8dd7-2e62677a290blogseq____",536870928]],[logseq____"^15logseq____",[322,logseq____"^Qlogseq____",logseq____"Übungsblätter abgebenlogseq____",536870928]],[logseq____"^15logseq____",[322,logseq____"^Ologseq____",logseq____"^16logseq____",536870928]],[logseq____"^15logseq____",[322,logseq____"^Flogseq____",321,536870928]],[logseq____"^15logseq____",[322,logseq____"^Xlogseq____",318,536870928]],[logseq____"^15logseq____",[322,logseq____"^Vlogseq____",321,536870928]],[logseq____"^15logseq____",[322,logseq____"^Ulogseq____",318,536870928]],[logseq____"^15logseq____",[322,logseq____"^17logseq____",true,536870928]],[logseq____"^15logseq____",[322,logseq____"^;logseq____",logseq____"~u6535b15d-5963-4ec0-8dbc-23ccc6e2c6cflogseq____",536870928]],[logseq____"^15logseq____",[323,logseq____"^Qlogseq____",logseq____"Übungsprüfungenlogseq____",536870928]],[logseq____"^15logseq____",[323,logseq____"^Ologseq____",logseq____"^16logseq____",536870928]],[logseq____"^15logseq____",[323,logseq____"^Flogseq____",322,536870928]],[logseq____"^15logseq____",[323,logseq____"^Xlogseq____",318,536870928]],[logseq____"^15logseq____",[323,logseq____"^Vlogseq____",321,536870928]],[logseq____"^15logseq____",[323,logseq____"^Ulogseq____",318,536870928]],[logseq____"^15logseq____",[323,logseq____"^17logseq____",true,536870928]],[logseq____"^15logseq____",[323,logseq____"^;logseq____",logseq____"~u6535b15d-c989-474a-8ce3-6c697599e2calogseq____",536870928]],[logseq____"^15logseq____",[325,logseq____"^Qlogseq____",logseq____"# Bedeutunglogseq____",536870929]],[logseq____"^15logseq____",[325,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[325,logseq____"^Flogseq____",241,536870929]],[logseq____"^15logseq____",[325,logseq____"^Xlogseq____",241,536870929]],[logseq____"^15logseq____",[325,logseq____"^Vlogseq____",241,536870929]],[logseq____"^15logseq____",[325,logseq____"^Ulogseq____",241,536870929]],[logseq____"^15logseq____",[325,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870929]],[logseq____"^15logseq____",[325,logseq____"^Jlogseq____",[],536870929]],[logseq____"^15logseq____",[325,logseq____"^17logseq____",false,536870929]],[logseq____"^15logseq____",[325,logseq____"^;logseq____",logseq____"~u6535b15d-7c98-4c84-817b-0eb4259f04b7logseq____",536870929]],[logseq____"^15logseq____",[326,logseq____"^Qlogseq____",logseq____"Q.E.D. = \\logseq____"quod erat demonstrandum\\logseq____"logseq____",536870929]],[logseq____"^15logseq____",[326,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[326,logseq____"^Flogseq____",325,536870929]],[logseq____"^15logseq____",[326,logseq____"^Xlogseq____",241,536870929]],[logseq____"^15logseq____",[326,logseq____"^Vlogseq____",325,536870929]],[logseq____"^15logseq____",[326,logseq____"^Ulogseq____",241,536870929]],[logseq____"^15logseq____",[326,logseq____"^17logseq____",true,536870929]],[logseq____"^15logseq____",[326,logseq____"^;logseq____",logseq____"~u6535b15d-0b5a-4a91-8f1c-c2fb6812e45blogseq____",536870929]],[logseq____"^15logseq____",[327,logseq____"^Qlogseq____",logseq____"lat. für \\logseq____"was zu beweisen wahr\\logseq____" (siehe [[w.z.b.w.]])logseq____",536870929]],[logseq____"^15logseq____",[327,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[327,logseq____"^Flogseq____",326,536870929]],[logseq____"^15logseq____",[327,logseq____"^Xlogseq____",241,536870929]],[logseq____"^15logseq____",[327,logseq____"^Vlogseq____",325,536870929]],[logseq____"^15logseq____",[327,logseq____"^Ulogseq____",241,536870929]],[logseq____"^15logseq____",[327,logseq____"^Ulogseq____",244,536870929]],[logseq____"^15logseq____",[327,logseq____"^Hlogseq____",244,536870929]],[logseq____"^15logseq____",[327,logseq____"^17logseq____",true,536870929]],[logseq____"^15logseq____",[327,logseq____"^;logseq____",logseq____"~u6535b15d-c7da-4c35-a3fc-d51396b9def4logseq____",536870929]],[logseq____"^15logseq____",[328,logseq____"^Qlogseq____",logseq____"Signalisiert das Ende eines Beweiseslogseq____",536870929]],[logseq____"^15logseq____",[328,logseq____"^Ologseq____",logseq____"^16logseq____",536870929]],[logseq____"^15logseq____",[328,logseq____"^Flogseq____",327,536870929]],[logseq____"^15logseq____",[328,logseq____"^Xlogseq____",241,536870929]],[logseq____"^15logseq____",[328,logseq____"^Vlogseq____",325,536870929]],[logseq____"^15logseq____",[328,logseq____"^Ulogseq____",241,536870929]],[logseq____"^15logseq____",[328,logseq____"^17logseq____",true,536870929]],[logseq____"^15logseq____",[328,logseq____"^;logseq____",logseq____"~u6535b15d-5703-42f0-9ccf-7f0385d33c5dlogseq____",536870929]],[logseq____"^15logseq____",[330,logseq____"^Klogseq____",1698017629156,536870930]],[logseq____"^15logseq____",[330,logseq____"^@logseq____",false,536870930]],[logseq____"^15logseq____",[330,logseq____"^Ylogseq____",logseq____"ungleichheitszeichenlogseq____",536870930]],[logseq____"^15logseq____",[330,logseq____"^11logseq____",logseq____"Ungleichheitszeichenlogseq____",536870930]],[logseq____"^15logseq____",[330,logseq____"^Blogseq____",1698017629156,536870930]],[logseq____"^15logseq____",[330,logseq____"^;logseq____",logseq____"~u6535b15d-8009-4421-a827-4e324d5ef1f2logseq____",536870930]],[logseq____"^15logseq____",[331,logseq____"^Klogseq____",1698017629157,536870930]],[logseq____"^15logseq____",[331,logseq____"^@logseq____",false,536870930]],[logseq____"^15logseq____",[331,logseq____"^Ylogseq____",logseq____"divisionlogseq____",536870930]],[logseq____"^15logseq____",[331,logseq____"^11logseq____",logseq____"Divisionlogseq____",536870930]],[logseq____"^15logseq____",[331,logseq____"^Blogseq____",1698017629157,536870930]],[logseq____"^15logseq____",[331,logseq____"^;logseq____",logseq____"~u6535b15d-9856-48a2-a4e9-8338acaa04a5logseq____",536870930]],[logseq____"^15logseq____",[332,logseq____"^Klogseq____",1698017629158,536870930]],[logseq____"^15logseq____",[332,logseq____"^@logseq____",false,536870930]],[logseq____"^15logseq____",[332,logseq____"^Ylogseq____",logseq____"multiplikationlogseq____",536870930]],[logseq____"^15logseq____",[332,logseq____"^11logseq____",logseq____"Multiplikationlogseq____",536870930]],[logseq____"^15logseq____",[332,logseq____"^Blogseq____",1698017629158,536870930]],[logseq____"^15logseq____",[332,logseq____"^;logseq____",logseq____"~u6535b15d-7c42-44a3-8737-2bd78b6cbfa9logseq____",536870930]],[logseq____"^15logseq____",[333,logseq____"^Qlogseq____",logseq____"# Regelnlogseq____",536870930]],[logseq____"^15logseq____",[333,logseq____"^Ologseq____",logseq____"^16logseq____",536870930]],[logseq____"^15logseq____",[333,logseq____"^Flogseq____",114,536870930]],[logseq____"^15logseq____",[333,logseq____"^Xlogseq____",114,536870930]],[logseq____"^15logseq____",[333,logseq____"^Vlogseq____",114,536870930]],[logseq____"^15logseq____",[333,logseq____"^Ulogseq____",114,536870930]],[logseq____"^15logseq____",[333,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870930]],[logseq____"^15logseq____",[333,logseq____"^Jlogseq____",[],536870930]],[logseq____"^15logseq____",[333,logseq____"^17logseq____",false,536870930]],[logseq____"^15logseq____",[333,logseq____"^;logseq____",logseq____"~u6535b15d-9216-431d-85e6-ed6f9703bf92logseq____",536870930]],[logseq____"^15logseq____",[334,logseq____"^Qlogseq____",logseq____"Bei [[Multiplikation]] oder [[Division]] mit einer negativen Zahl wird das [[Ungleichheitszeichen]] umgekehrtlogseq____",536870930]],[logseq____"^15logseq____",[334,logseq____"^Ologseq____",logseq____"^16logseq____",536870930]],[logseq____"^15logseq____",[334,logseq____"^Flogseq____",333,536870930]],[logseq____"^15logseq____",[334,logseq____"^Xlogseq____",114,536870930]],[logseq____"^15logseq____",[334,logseq____"^Vlogseq____",333,536870930]],[logseq____"^15logseq____",[334,logseq____"^Ulogseq____",114,536870930]],[logseq____"^15logseq____",[334,logseq____"^Ulogseq____",330,536870930]],[logseq____"^15logseq____",[334,logseq____"^Ulogseq____",331,536870930]],[logseq____"^15logseq____",[334,logseq____"^Ulogseq____",332,536870930]],[logseq____"^15logseq____",[334,logseq____"^Hlogseq____",330,536870930]],[logseq____"^15logseq____",[334,logseq____"^Hlogseq____",331,536870930]],[logseq____"^15logseq____",[334,logseq____"^Hlogseq____",332,536870930]],[logseq____"^15logseq____",[334,logseq____"^17logseq____",true,536870930]],[logseq____"^15logseq____",[334,logseq____"^;logseq____",logseq____"~u6535b15d-d3d8-4691-a125-fd2196fa4edclogseq____",536870930]],[logseq____"^15logseq____",[335,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\logseq____"logseq____>\\logseq____"logseq____&\\\\rightarrow\\logseq____"logseq____<\\logseq____"\\\\\\\\\\n\\logseq____"logseq____<\\logseq____"logseq____&\\\\rightarrow\\logseq____"logseq____>\\logseq____"\\\\\\\\\\n\\logseq____"\\\\ge\\logseq____"logseq____&\\\\rightarrow\\logseq____"\\\\le\\logseq____"\\\\\\\\\\n\\logseq____"\\\\le\\logseq____"logseq____&\\\\rightarrow\\logseq____"\\\\ge\\logseq____"\\\\\\\\\\n\\\\end{align}logseq____",536870930]],[logseq____"^15logseq____",[335,logseq____"^Ologseq____",logseq____"^16logseq____",536870930]],[logseq____"^15logseq____",[335,logseq____"^Flogseq____",334,536870930]],[logseq____"^15logseq____",[335,logseq____"^Xlogseq____",114,536870930]],[logseq____"^15logseq____",[335,logseq____"^Vlogseq____",334,536870930]],[logseq____"^15logseq____",[335,logseq____"^Ulogseq____",114,536870930]],[logseq____"^15logseq____",[335,logseq____"^Ulogseq____",330,536870930]],[logseq____"^15logseq____",[335,logseq____"^Ulogseq____",331,536870930]],[logseq____"^15logseq____",[335,logseq____"^Ulogseq____",332,536870930]],[logseq____"^15logseq____",[335,logseq____"^17logseq____",true,536870930]],[logseq____"^15logseq____",[335,logseq____"^;logseq____",logseq____"~u6535b15d-f9b3-4b6b-a9f7-450007b36f9alogseq____",536870930]],[logseq____"^15logseq____",[336,logseq____"^Qlogseq____",logseq____"logseq____",536870930]],[logseq____"^15logseq____",[336,logseq____"^Ologseq____",logseq____"^16logseq____",536870930]],[logseq____"^15logseq____",[336,logseq____"^Flogseq____",335,536870930]],[logseq____"^15logseq____",[336,logseq____"^Xlogseq____",114,536870930]],[logseq____"^15logseq____",[336,logseq____"^Vlogseq____",334,536870930]],[logseq____"^15logseq____",[336,logseq____"^Ulogseq____",114,536870930]],[logseq____"^15logseq____",[336,logseq____"^Ulogseq____",330,536870930]],[logseq____"^15logseq____",[336,logseq____"^Ulogseq____",331,536870930]],[logseq____"^15logseq____",[336,logseq____"^Ulogseq____",332,536870930]],[logseq____"^15logseq____",[336,logseq____"^17logseq____",true,536870930]],[logseq____"^15logseq____",[336,logseq____"^;logseq____",logseq____"~u6535b15d-88f1-4b98-b604-b1df6690b4d8logseq____",536870930]],[logseq____"^15logseq____",[338,logseq____"^Klogseq____",1698017629172,536870931]],[logseq____"^15logseq____",[338,logseq____"^@logseq____",false,536870931]],[logseq____"^15logseq____",[338,logseq____"^Ylogseq____",logseq____"vorlesungs notizenlogseq____",536870931]],[logseq____"^15logseq____",[338,logseq____"^11logseq____",logseq____"Vorlesungs Notizenlogseq____",536870931]],[logseq____"^15logseq____",[338,logseq____"^Blogseq____",1698017629172,536870931]],[logseq____"^15logseq____",[338,logseq____"^;logseq____",logseq____"~u6535b15d-8420-44ac-be52-021c818a2ed6logseq____",536870931]],[logseq____"^15logseq____",[339,logseq____"^Qlogseq____",logseq____"[[Auffrischung Mathematik]]logseq____",536870931]],[logseq____"^15logseq____",[339,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[339,logseq____"^Flogseq____",338,536870931]],[logseq____"^15logseq____",[339,logseq____"^Xlogseq____",338,536870931]],[logseq____"^15logseq____",[339,logseq____"^Vlogseq____",338,536870931]],[logseq____"^15logseq____",[339,logseq____"^Ulogseq____",24,536870931]],[logseq____"^15logseq____",[339,logseq____"^Ulogseq____",338,536870931]],[logseq____"^15logseq____",[339,logseq____"^Hlogseq____",24,536870931]],[logseq____"^15logseq____",[339,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[339,logseq____"^;logseq____",logseq____"~u6535b15d-6d2d-4aaf-89fa-0bc9a062568dlogseq____",536870931]],[logseq____"^15logseq____",[340,logseq____"^Qlogseq____",logseq____"[[Mathematik für Informatiker 1]]logseq____",536870931]],[logseq____"^15logseq____",[340,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[340,logseq____"^Flogseq____",339,536870931]],[logseq____"^15logseq____",[340,logseq____"^Xlogseq____",338,536870931]],[logseq____"^15logseq____",[340,logseq____"^Vlogseq____",338,536870931]],[logseq____"^15logseq____",[340,logseq____"^Ulogseq____",307,536870931]],[logseq____"^15logseq____",[340,logseq____"^Ulogseq____",338,536870931]],[logseq____"^15logseq____",[340,logseq____"^Hlogseq____",307,536870931]],[logseq____"^15logseq____",[340,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[340,logseq____"^;logseq____",logseq____"~u6535b15d-d229-439d-812e-8b415065cffalogseq____",536870931]],[logseq____"^15logseq____",[341,logseq____"^Qlogseq____",logseq____"[[Grundlagen und Diskrete Strukturen]]logseq____",536870931]],[logseq____"^15logseq____",[341,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[341,logseq____"^Flogseq____",340,536870931]],[logseq____"^15logseq____",[341,logseq____"^Xlogseq____",338,536870931]],[logseq____"^15logseq____",[341,logseq____"^Vlogseq____",338,536870931]],[logseq____"^15logseq____",[341,logseq____"^Ulogseq____",187,536870931]],[logseq____"^15logseq____",[341,logseq____"^Ulogseq____",338,536870931]],[logseq____"^15logseq____",[341,logseq____"^Hlogseq____",187,536870931]],[logseq____"^15logseq____",[341,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[341,logseq____"^;logseq____",logseq____"~u6535b15d-8e64-4810-885c-eb84ab1d20e5logseq____",536870931]],[logseq____"^15logseq____",[342,logseq____"^Qlogseq____",logseq____"[[Programmierung und Algorithmen]]logseq____",536870931]],[logseq____"^15logseq____",[342,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[342,logseq____"^Flogseq____",341,536870931]],[logseq____"^15logseq____",[342,logseq____"^Xlogseq____",338,536870931]],[logseq____"^15logseq____",[342,logseq____"^Vlogseq____",338,536870931]],[logseq____"^15logseq____",[342,logseq____"^Ulogseq____",318,536870931]],[logseq____"^15logseq____",[342,logseq____"^Ulogseq____",338,536870931]],[logseq____"^15logseq____",[342,logseq____"^Hlogseq____",318,536870931]],[logseq____"^15logseq____",[342,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[342,logseq____"^;logseq____",logseq____"~u6535b15d-ec5d-4b75-9730-c89688e40779logseq____",536870931]],[logseq____"^15logseq____",[343,logseq____"^Qlogseq____",logseq____"logseq____<iframe src=\\logseq____"https://cal.lu-dev.de\\logseq____" style=\\logseq____"width: 100%; height: 1220px\\logseq____"logseq____>logseq____</iframelogseq____>logseq____",536870931]],[logseq____"^15logseq____",[343,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[343,logseq____"^Flogseq____",342,536870931]],[logseq____"^15logseq____",[343,logseq____"^Xlogseq____",338,536870931]],[logseq____"^15logseq____",[343,logseq____"^Vlogseq____",338,536870931]],[logseq____"^15logseq____",[343,logseq____"^Ulogseq____",338,536870931]],[logseq____"^15logseq____",[343,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[343,logseq____"^;logseq____",logseq____"~u6535b15d-7947-4215-b04d-67583dc9dc19logseq____",536870931]],[logseq____"^15logseq____",[344,logseq____"^Qlogseq____",logseq____"logseq____",536870931]],[logseq____"^15logseq____",[344,logseq____"^Ologseq____",logseq____"^16logseq____",536870931]],[logseq____"^15logseq____",[344,logseq____"^Flogseq____",343,536870931]],[logseq____"^15logseq____",[344,logseq____"^Xlogseq____",338,536870931]],[logseq____"^15logseq____",[344,logseq____"^Vlogseq____",338,536870931]],[logseq____"^15logseq____",[344,logseq____"^Ulogseq____",338,536870931]],[logseq____"^15logseq____",[344,logseq____"^17logseq____",true,536870931]],[logseq____"^15logseq____",[344,logseq____"^;logseq____",logseq____"~u6535b15d-b3a6-43d8-87f5-991b042f633dlogseq____",536870931]],[logseq____"^15logseq____",[346,logseq____"^Qlogseq____",logseq____"# Bedeutunglogseq____",536870932]],[logseq____"^15logseq____",[346,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[346,logseq____"^Flogseq____",244,536870932]],[logseq____"^15logseq____",[346,logseq____"^Xlogseq____",244,536870932]],[logseq____"^15logseq____",[346,logseq____"^Vlogseq____",244,536870932]],[logseq____"^15logseq____",[346,logseq____"^Ulogseq____",244,536870932]],[logseq____"^15logseq____",[346,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870932]],[logseq____"^15logseq____",[346,logseq____"^Jlogseq____",[],536870932]],[logseq____"^15logseq____",[346,logseq____"^17logseq____",false,536870932]],[logseq____"^15logseq____",[346,logseq____"^;logseq____",logseq____"~u6535b15d-8e47-460b-941b-148f0a3e5555logseq____",536870932]],[logseq____"^15logseq____",[347,logseq____"^Qlogseq____",logseq____"w.z.b.w. = \\logseq____"was zu beweisen war\\logseq____"logseq____",536870932]],[logseq____"^15logseq____",[347,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[347,logseq____"^Flogseq____",346,536870932]],[logseq____"^15logseq____",[347,logseq____"^Xlogseq____",244,536870932]],[logseq____"^15logseq____",[347,logseq____"^Vlogseq____",346,536870932]],[logseq____"^15logseq____",[347,logseq____"^Ulogseq____",244,536870932]],[logseq____"^15logseq____",[347,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[347,logseq____"^;logseq____",logseq____"~u6535b15d-f5a8-4f23-b0ff-c42be1384a75logseq____",536870932]],[logseq____"^15logseq____",[348,logseq____"^Qlogseq____",logseq____"Signalisiert das Ende eines Beweiseslogseq____",536870932]],[logseq____"^15logseq____",[348,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[348,logseq____"^Flogseq____",347,536870932]],[logseq____"^15logseq____",[348,logseq____"^Xlogseq____",244,536870932]],[logseq____"^15logseq____",[348,logseq____"^Vlogseq____",346,536870932]],[logseq____"^15logseq____",[348,logseq____"^Ulogseq____",244,536870932]],[logseq____"^15logseq____",[348,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[348,logseq____"^;logseq____",logseq____"~u6535b15d-52a8-4775-b94d-63ce20c4b82blogseq____",536870932]],[logseq____"^15logseq____",[349,logseq____"^Qlogseq____",logseq____"siehe [[Q.E.D.]]logseq____",536870932]],[logseq____"^15logseq____",[349,logseq____"^Ologseq____",logseq____"^16logseq____",536870932]],[logseq____"^15logseq____",[349,logseq____"^Flogseq____",348,536870932]],[logseq____"^15logseq____",[349,logseq____"^Xlogseq____",244,536870932]],[logseq____"^15logseq____",[349,logseq____"^Vlogseq____",346,536870932]],[logseq____"^15logseq____",[349,logseq____"^Ulogseq____",241,536870932]],[logseq____"^15logseq____",[349,logseq____"^Ulogseq____",244,536870932]],[logseq____"^15logseq____",[349,logseq____"^Hlogseq____",241,536870932]],[logseq____"^15logseq____",[349,logseq____"^17logseq____",true,536870932]],[logseq____"^15logseq____",[349,logseq____"^;logseq____",logseq____"~u6535b15d-513d-4323-845e-b17b50055f1flogseq____",536870932]],[logseq____"^15logseq____",[351,logseq____"^Klogseq____",1698017629191,536870933]],[logseq____"^15logseq____",[351,logseq____"^@logseq____",false,536870933]],[logseq____"^15logseq____",[351,logseq____"^Ylogseq____",logseq____"readmelogseq____",536870933]],[logseq____"^15logseq____",[351,logseq____"^11logseq____",logseq____"READMElogseq____",536870933]],[logseq____"^15logseq____",[351,logseq____"^Blogseq____",1698017629191,536870933]],[logseq____"^15logseq____",[351,logseq____"^;logseq____",logseq____"~u6535b15d-17c1-40d8-9ffa-d560f75b8396logseq____",536870933]],[logseq____"^15logseq____",[352,logseq____"^Qlogseq____",logseq____"Branch for autogenerated assets that are accessed through through raw.githubusercontents.com\\nlogseq____",536870933]],[logseq____"^15logseq____",[352,logseq____"^Ologseq____",logseq____"^16logseq____",536870933]],[logseq____"^15logseq____",[352,logseq____"^Flogseq____",351,536870933]],[logseq____"^15logseq____",[352,logseq____"^Xlogseq____",351,536870933]],[logseq____"^15logseq____",[352,logseq____"^Vlogseq____",351,536870933]],[logseq____"^15logseq____",[352,logseq____"^Ulogseq____",351,536870933]],[logseq____"^15logseq____",[352,logseq____"^:logseq____",true,536870933]],[logseq____"^15logseq____",[352,logseq____"^Jlogseq____",[],536870933]],[logseq____"^15logseq____",[352,logseq____"^17logseq____",true,536870933]],[logseq____"^15logseq____",[352,logseq____"^;logseq____",logseq____"~u6535b15d-6b96-4b5e-ab6d-8adc0b9ef109logseq____",536870933]]]]]]"</script>
<script>window.logseq_state="{:ui/theme \"dark\", :config {\"local\" {:shortcuts {}, :default-templates {:journals \"\"}, :feature/enable-journals? false, :query/views {:pprint (fn [r] [:pre.code (pprint r)])}, :editor/preferred-pasting-file? true, :macros {}, :shortcut/doc-mode-enter-for-new-block? false, :favorites [], :ui/show-empty-bullets? false, :file/name-format :triple-lowbar, :preferred-workflow :now, :publishing/all-pages-public? true, :ref/default-open-blocks-level 2, :feature/enable-block-timestamps? false, :start-of-week 6, :ref/linked-references-collapsed-threshold 50, :outliner/block-title-collapse-enabled? false, :commands [], :ui/show-full-blocks? false, :meta/version 1, :hidden [], :default-queries {:journals [{:title \"🔨 NOW\", :query [:find (pull ?h [*]) :in $ ?start ?today :where [?h :block/marker ?marker] [(contains? #{\"NOW\" \"DOING\"} ?marker)] [?h :block/page ?p] [?p :block/journal? true] [?p :block/journal-day ?d] [(>= ?d ?start)] [(<= ?d ?today)]], :inputs [:14d :today], :result-transform (fn [result] (sort-by (fn [h] (get h :block/priority \"Z\")) result)), :group-by-page? false, :collapsed? false} {:title \"📅 NEXT\", :query [:find (pull ?h [*]) :in $ ?start ?next :where [?h :block/marker ?marker] [(contains? #{\"NOW\" \"LATER\" \"TODO\"} ?marker)] [?h :block/page ?p] [?p :block/journal? true] [?p :block/journal-day ?d] [(> ?d ?start)] [(< ?d ?next)]], :inputs [:today :7d-after], :group-by-page? false, :collapsed? false}]}, :ui/auto-expand-block-refs? true, :ui/enable-tooltip? true, :query/result-transforms {:sort-by-priority (fn [result] (sort-by (fn [h] (get h :block/priority \"Z\")) result))}, :property-pages/enabled? true, :block/content-max-length 10000, :ui/show-command-doc? true, :feature/enable-search-remove-accents? true, :default-home {:page \"Vorlesungs Notizen\"}}}}"</script>
<script type="text/javascript">// Single Page Apps for GitHub Pages
// https://github.com/rafgraph/spa-github-pages