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Zusammenfassung Analysis1
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ANALYSIS 1,O .
Allgemeine Grundbegriffe
Das Prinzip der Induktion
0 1
.
vollständigen
(1) A(1) ist
It :
richtig .
(2) IS :
A(n) =
>A(n + 1)
0 2 .
Grundbegriffe der
Mengenlehre
(i) AmB : =
EX : xA und xEB) Schnitt
(ii) AuB :=
Ex :
XEA oder x = B)
Vereinigung
(iii) AnBeC := Ex : XeA und xEB und xECh
Für
beliebig viele
Mengen
:
Fassen wir diese
beliebig A definieren
viele
Mengen zu zusammen , so wir
A : =
EX XAFA :
bzW .
:= Ex :
Jet mit A
(iv) A und B heißen disjunkt ,
falls
AnB S =
= A + B statt AuB
(V) A heißt
Teilmenge von B , falls
x (A = XEB
ACB =
BJ A (B Obermenge von Al
(vi) A B :
,
falls
ACB und BCA ,
dh . .
xEAlsXEB
(vii) P(B) : =
GA ACB3 >
Potenzmenge
-
:
Bsp .: B =
(4 b) ,
P(B) (54 63 593
=
, , ,
463 , 03
(viii) AlB : = EX : XA und xEB)
Ist ACX ,
ist XIA AS
(ix) AxB : =
((a b) ,
:
= p( A ,
beB]
↳ kartesisches Produkt
Kommutativgesetze
ArB = BnA
,
AuB =
Bra
Assoziativgesetze
(AnBInC AnBBnC) = und (AvBluC ArIBUC]=
Distributivgesetze
(AnBluC =
(Arc)e (BUC) um & LAUBInC =
(AnClvlBeC)
de Morgansche RegeIn
AcX = <
(A))" = A
A vB = (AIB) + (AnB) + (BIA)
AnB Ac=> AcB = und AuB =
BEs ACB
A , B(X =
) (AnBl A'vBC =
und lAUB)" = ABS
1
,
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