Need a formal proof?

Question

If A and B are two equipotent sets (they have 1-1 correspondence). Prove that if A is denumerable then B is also denumerable. It is easy to understand by intuition. But I can't understand how to prove it formally.

Answer 1

Since $A$ is denumerable there is a biiection $f \colon \mathbb N \to A$. By hypothesis there is a biiection $g\colon A \to B$, since composition of biiection is a biiection we have that $g \circ f \colon \mathbb N \to B$ is a biiection too, hence $B$ is denumerable.