5. Let $f: Z \to \mathbb{N}_0$ be a function defined by $f(n) = |n|$ for all $n \in Z$ where Z is the set of
integers
$Z = \{..., -n, ..., -3, -2, -1, 0, 1, 2, 3, ..., n, ...\}$
and $\mathbb{N}_0$ is the set of nonnegative integers.
$\mathbb{N}_0 = \{0, 1, 2, 3, ..., n, ...\}$
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
$\frac{(integer)}{(integer)}$
where the denominator is a nonzero integer.
