Prove $\mathbb{Z}^n$ is countable. Prove $\mathbb{Z}^n$ is countable.
My attempt:
We know $\mathbb{N}$ is a countable set (trivial)
Moreover, $\mathbb{Z}$ is a countable set because we can construct a bijective function in $\mathbb{N}\rightarrow \mathbb{Z}$ such that 
I have stuck because i want prove $\mathbb{Z^n}$ is countable.
Can someone help me?

Hint: You know $\mathbb{N}$ is countable, then $\mathbb{N}\times\mathbb{N}$ is countable you can prove that exists a bijective function $\mathbb{N}\times\mathbb{N}$ to $\mathbb{Z}\times\mathbb{Z}$ and then use induction for prove for $\mathbb{Z}\times...\times\mathbb{Z}$
