elementary set theory - Proving $rm{card}(Bbb Z)=rm{card}(Bbb N)$

So I'm trying to prove that the set of integers has the same cardinality as the set of naturals just using the definition, that is, I'm trying to find a bijective function between the two sets. I found this Why do the rationals, integers and naturals all have the same cardinality? but I couldn't quite find the answer.

Thanks for any help.

Answer

HINT(ish):

Let $f:\mathbb Z\to\mathbb N$ be the bijection in question, $f(0)=0$, and for any natural number $n$, let $f(n)=2n$. Can you complete the construction for what the negative integers are mapped to?