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W{+H`cPGw+VVDNPHb6Mw<&;$T*{qn*9 literal 0 HcmV?d00001 diff --git a/kurs-notering.txt b/kurs-notering.txt index 0a680ce..85fc08f 100644 --- a/kurs-notering.txt +++ b/kurs-notering.txt @@ -3,3 +3,4 @@ skret Matematik Tentamen i Oktober 2 övnings pass / vecka +Fins lista av rekomenderade upgifter, och gamla tentor diff --git a/notes-sep-1.txt b/notes-sep-1.txt index 57827bf..6d641d8 100644 --- a/notes-sep-1.txt +++ b/notes-sep-1.txt @@ -12,7 +12,7 @@ Grundbegrepp: - |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 + - Delmänd: "c" med understrek, används när vi inte kan bevisa att alla element i A fins 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 @@ -23,10 +23,50 @@ Grundbegrepp: - 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: + - A är en mänd av elementen {5, 7, 9}, B är en mänd av {9, 5, 7, 3}, där C = {9, 5, 7} och D = {5, 7, 3}, där C c B, och D c B men inte C c B eller B c C - 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 + - A = {{ }}, då är A en mänd av ø, |A| = 1, A != ø +- Mänder är inte tal! + - Skriv inte A = 3, om fallet av kordinalitet skall det skrivas |A| = 3 +- En mängd kan vara ett element + - Example A = {{1, 2}, {a, b}}, |A| = 2, {1,2} € A, 1 !€ A, {{1, 2}} c A Talmängder: +- De natuliga talen: N = {0, 1, 2, ...} +- De hela talen: Z = {..., -2, -1, 0, 1, 2, ...} +- De rationella talen: Q = {p/q: p,q € Z, q != 0}, Ex: 5/3 +- De reela talen: R = Q u {de irratonella talen} Ex: irratinella tal pi, e, sqrt(2) +- De complexa talen: C = {x+iy : x,y € R, i^2 = -1} +- N c Z c Q c R c C +- u - eller, u(upp och ner) - och, c - delmänd till, € tillhör +Intervall: +- Alla tal mellan två uppgivna tal +- Slutet intervall: [a, b] = {x € R : a <= x <= b} +- Öppen intervall: + - (a, b) = ]a,b[ = {x € R : a < x < b} + - (-inf, b) = ]-inf, b[ = {x € R : x < b} + - (a, inf) = ]a, -ind[ = {x € R : a < x} + - (-inf, inf) = ]-inf, inf[ = R +- Halv öppen intervall: + - (a, b] = ]a, b] = {x € R : a < x <= b} + - [a, b) = [a, b) = {x € R : a <= x < b} + - (-inf, b] = ]-inf, b] = {x € R : x <= b} + - [a, inf) = [a, inf) = {x € R : a <= x} Mängdoperationer: +- Grundmänd (Universual set): U + - tom mänd: ø = {}, ø …c A …c U för varje mängd A +- Union: A u B = {x € U|x € A eller x € B} +- Snitt: A ↓u B = {x € U|x € A och x € B} +- Komplement: A^c = ¨A = {x € U|x !€ A} + - ¨U = ø och ¨ø = U +- Differens: A\B = {a U B = (A u B)\(A ↓u B) +- + - A = {5, 7, 3} + - B = {3, 5, 7} + - A u B = {3, 5, 7, 9} + - A ↓u B = {5, 7} + - U = {1, 3, 5, 7, 9} + - A^c = {1, 2} + - B^c = {1, 9}