关于双射的证明(2) f:ZN explicitly as follows: f-{2+2 2x ifx≥0 otherwise Proof that f maps Z onto N. Letk∈N.If k is even,then k=2 m for some m∈Z with m≥O. Thus,m eZ and f(m)=2m k.If k is odd,then k+1 is even. Hence m=(k+1)/(-2)∈Z.Since k≥1，we have m<0.Thus, f(m)=-2m-1 =-2((k +1)/(-2))-1 k.We conclude that for allk∈N,there exists m∈Z such that f(m)=k.Sincef:Z→Nis a well-defined function,f maps Z onto N. ■关于双射的证明 (2)