5.1 5.2 5.3 5.4

5.1 5.1.1 ABFABxAyBFFABF:ABAFD(F)=ABFR(F)FR(F)BF(A)F

F(A)=R(F)={y|yB(x)(xAy=F(x))}F(A)FF:ABFxyyxyFxyFxFF(x)=y

ABFAB AF F(x)=yFxF(x)=yF(x)=zy=zFf

5.1.2 f:ABg:CDA=CB=DxAf(x)=g(x)fgf=g

5.1.3 f:ABCAg=f(CB)gfCf|cgCBg:CBg(x)=f(x) f|c(x)=f(x)5.1.4 f:CBg:ABCAg|c=fgfA

ABf:ABABBABA={f|f:AB}|A|=m|B|=n|BA|=nmnnmAB

5.1.5 A1,A2,,AnBf: AiBf nf(x1,x2,,xn)n

5.2

5.2.1 f:ABR(f)=BbBaAf(a)=b(y)(yB(x)(xAf(x)=y))f:ABf:ABfBbAaABf:AB|A||B|

5.2.2 f:ABabAabf(a)f(b)(x)(y)(x,yAxyf(x)f(y))f:ABf:ABABABf:AB|A||B|

5.2.3 f:ABff:ABf:ABBbAaABf:AB|A|=|B|

5.2.4 f:ABbBaAf(a)=bf(A)={b}f:AB

5.2.5 f:AAaAf(a)=af={|xA}f:AAAIAAIA

5.2.6 ABABA:B{0,1} 1 xA xA(x)= 0 xAA

{

5.2.1 ABUxU A(x)=0A= A(x)=1A=U

A(x)B(x)AB A(x)=B(x)A=B A(x)=1-A(x) AB(x)=xA(x)*xB(x) AB(x)=A(x)+B(x)-AB(x) A-B(x)=AB(x)=A(x)-AB(x)+-*+-

5.2.7 f:ABa,bA. abf(a)f(b)f abf(a)f(b)f

ababf(a)f(b)f

5.2.8 RAf:AA/Rf(a)=[a]RaAfAA/R5.2.9 p:AAppA

5.3

15.3.1 f:ABg:BCoACgofaA(gof)(x)=g(f(x))

ogoffogfoggof=fog

1 f,g,h(fog)oh=fo(goh)Af:AAffn f 0(x)=x f n+1(x)=f(fn(x))nN

5.3.2 f:ABg:BC f:ABg:BCgof:AC f:ABg:BCgof:AC f:ABg:BCgof:AC

5.3.3 f:ABf=foIA=IBoff:AAfoIA= IAof=f

2RA={a,b,c}B={1,2,3}f={,,}f-1={,,}BAf:ABf-1BA5.3.4 f:ABf-1:BA

5.3.1 f:AB f -1:BAff-1f5.3.5 f:AB f -1of=IAfof-1=IB5.3.6 f:AB(f-1)-1=f

5.4 1Nn={0,1,2,,n-1}N

5.4.1 Af:NnAAAn|A|=ncard A=nAAAA5.4.1 NN

5.4.2 Af:NAA0|A|=0NN|N|=000f:NnAA

5.4.3 Af:NnAA|A|=0AAA

5.4.2 A1,A2,A3, Ai NnNNnnN00

25.4.4 ABABABAB|A|=|B|AB

ABAB|A||B|ABAB|A|

5.4.3

3{{a,b,c},{p,q,r},{1,2,3},}0N

ABABBAB

5.4.4 ZermeloAB |A|

5.4.5 Cantor-Schroder-BernsteinAB|A||B||B||A||A|=|B|f:AB|A||B|g:BC|B||A||A|=|B|fg

5.4.6 A|A|

5.4.8 CantorA|A|