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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
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.
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