proof: set countable iff there is a bijection In class we had the following definiton of a countable set:
A set $M$ is countable if there is a bijection between $\mathbb N$ and $M$.
In our exam today, we had the following thesis given:If $A$ is a countable set, then there is a bijection $\mathbb N\rightarrow A$. 
So I am really not sure if the thesis and therefore the equivalence in the definition is right. So is it correct? And how do you proove it? Thanks a lot!

Suppose that $A$ is countable by your definition; then there is a bijection $f:\Bbb N\to A$. Because $f$ is a bijection, $f^{-1}$ is also a bijection, so it’s the desired bijection from $A$ to $\Bbb N$.
