1 Prove the following function is a bijection Let f ZZ by f

1. Prove the following function is a bijection. Let f : ZZ by f(n) = 2n for all n Z.

Solution

let f(n1) = f(n2)

=>

2-n1 = 2-n2

=>
n1 = n2

=>

f is one-one.............(1)

f(2-n) = 2-(2-n) = n

=>

f is onto .................(2)

(1) ,(2) implies

f is bijection

thus proved