Prove that $\mathbb{N}$ has the same cardinality as $\mathbb{Z}^4$.
I was thinking of construct a bijection from $\mathbb{N}$ to $\mathbb{Z}^4$, and a way which I think can be used is combining a bijection from $\mathbb{N}$ to $\mathbb{Z}^2$ and a bijection from $\mathbb{Z}$ to $\mathbb{Z}^2$. And I stuck here.
Thanks for any and all help.
Hint: Have a look at Cantor's pairing function.
The basic idea is that, by forming an array, you can wind your way around and get a bijection between the cross product of a countable set with itself and $\Bbb N$ (or $\Bbb Z$). The point is that it's countable.