Is there a bijection between $\mathbb N$ and $\mathbb N^2$? 
Is there a bijection between $\mathbb N$ and $\mathbb N^2$?

If I can show $\mathbb N^2$ is equipotent to $\mathbb N$, I can show that $\mathbb Q$ is countable. Please help. Thanks,

You're trying to find a way to "count" the things in $\mathbb N^2$ in a manner that gets you to any pair $(a,b)$ in some finite time. Notice that "counting" something is essentially finding this bijection - there is a "first" pair, and a "second pair" and so on.
There are many ways to do this, but most of them come down to ordering the set $\mathbb N^2$ in some meaningful way. 
Hint: There are countably many diagonals, i.e. there is a "first diagonal" a "second diagonal" and so on. Does this work? 
