关于双射的证明(2) f ZN explicitly as follows: ifx≥0 -1+2) otherwise Proof that f maps Z onto N. Letk∈N.If k is even,then k=2 m for some m∈Z with m≥0. Thus,m e Z and f(m)=2m k.If k is odd,then k+1 is even. Hence m =(k+1)/(-2)EZ.Since k z 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.Since f:Z→Nis a well-defined function,f maps Z onto N. ■关于双射的证明 (2)