From 8a1769e7b8946457ba4356cfd916d5c8f4279735 Mon Sep 17 00:00:00 2001 From: zacharias Date: Mon, 1 Sep 2025 11:04:35 +0200 Subject: [PATCH] sep-1-11_00 --- kurs-notering.txt | 5 +++++ notes-sep-1.txt | 27 +++++++++++++++++++++++++++ venn_diagram.png | Bin 0 -> 256849 bytes 3 files changed, 32 insertions(+) create mode 100644 kurs-notering.txt create mode 100644 venn_diagram.png diff --git a/kurs-notering.txt b/kurs-notering.txt new file mode 100644 index 0000000..0a680ce --- /dev/null +++ b/kurs-notering.txt @@ -0,0 +1,5 @@ +skret Matematik + +Tentamen i Oktober +2 övnings pass / vecka + diff --git a/notes-sep-1.txt b/notes-sep-1.txt index 12be2a9..57827bf 100644 --- a/notes-sep-1.txt +++ b/notes-sep-1.txt @@ -1,5 +1,32 @@ Mänger 1 Grundbegrepp: +- En Mänd är en lista av element +- Lister betäknas med stora boktäver som A = {1,2,3} eller A = {x: x|120} (Betyder alla X sådant att X möter ett krav, exampel X skall delas jämt med 120), element beteknas med små bokstäver +- Ej ordning, ej upprepning. {1,2,3} = {1,2} = {2,1} +- Betekning "€"(epilon): tillhör +- "|" betyder delas jämt med, (X % Y == 0) +- Väldefinerad: A = {5, 7, 9}, 5€A, "€" betyder "tillhör" som att 5 tillhör listan A + - Alla mänder(listor) skall vara tydligt definerade, för att unvika sitvationer där ett element kan både tillhöra och inte tillhöra en mänd +- Kardinalitet: |A| betyder läng(antal element) i listan A + - |A| är antigen heltal eller oendlig + - Example A = {1, 2, 3}, så är |A| = 3, medans B = {x : x|2}, så är |B| = oendlig +- Delmängd: + - Delmänd: "c" med understrek, används när några element find i A som find i B + - Äkta delmänd: "c", används bara om alla emenent i A fins i B + - Om det går att bevisa att alla element i A find i B skall c änvändas och inte …c + - Om A …c B och B …c A, så är A = B + - Example + - A = {2, 3} B = {1, 2, 3}, så är A c B, Alla element i A find i B + - A = {3, 7, 9}, B = {3, 5, 7}, |A| = 3, |B| = 3, A !c B, eftersom inte alla element i A find i B, samt B !c A eftersom inte alla element i B fins i A + - A c B och B c A måste inte båda vara sanna, utan kan bara vara sanna om |A| == |B|, och A c B + - A = {3, 7, 9}, B = {3, 5, 7}, C = {1, 3, 5, 7, 9}, då är A c C, B c C, men C !c A, C !c B, och A !c B +- Rita mänder + - Venn Diagram: +- Null-set/nollmänd/Empty set + - en tom lista, där |A| = 0 + - "ø"(fii) = { } + - "ø" …c A, för varje mänd A + - A = {{ }}, då är A en mänd av ø Talmängder: Mängdoperationer: diff --git a/venn_diagram.png b/venn_diagram.png new file mode 100644 index 0000000000000000000000000000000000000000..96971fa5766ec786b250f51cc76342921ad13185 GIT binary patch literal 256849 zcmeAS@N?(olHy`uVBq!ia0y~y;M~B#z`KQmje&tdZ_iI&1_lPs0*}aI1_nK45N51c zYG1~{puphi;uum9_vY^Y)8~K7AOASL`JB9iBDd>KHswtxwA>a4-ca4B@$~qToKy21 zc{_U?NJNw=}-}L11^6d|M z85o&ZI0O_N8VE6bA|CW}zMrW~SS8f7covo%zD7dELKU+JF)~IU%9}#0a+aJtf-W94 z8b=U~hBaCu9u1Ju0Ks1lj;4^&6f&AZSVpT|v}`aMAfo|-zg!qiA)_f|G=+?I?ofKR 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