Consider the functionf:

f:NZdefined byf(n)=(1n)/2

f(n)=(1n)/2whenn

nis odd andf(n)=n/2

f(n)=n/2whenn

nis even. Prove thatf

fis bijective by proving that it has a two-sided inverse. In other words, carefully define a functiong:

g:ZNand prove thatfg

fgandgf

gfare both identity functions.