Let f:Z->N_(0) be a function defined by f(n)=|n| for all ninZ where Z is the set of
integers
Z={dots,-n,dots,-3,-2,-1,0,1,2,3,dots,n,dots}
and N_(0) is the set of nonnegative integers.
N_(0)={0,1,2,3,dots,n,dots}
a) Prove that f is onto (surjective).
b) Prove that f is not one-to-one.
^(1) We say a number is rational number if it can be written as
( (integer) )/( (integer) )
where the denominator is a nonzero integer.
5. Let f : Z -> No be a function defined by f(n) = |n| for all n E Z where Z is the set of integers Z ={...,--n,....,--3,--2,--1,0,1,2,3,...,n,...} and No is the set of nonnegative integers.
No={0,1,2,3,...,n,...)
a) Prove that f is onto (surjective). b) Prove that f is not one-to-one.
1We say a number is rational number if it can be written as (integer) (integer) where the denominator is a nonzero integer. 1