A homework question asks the following:
"Let $X$ be a countable, not finite set. Show that there is a bijection $\phi :\mathbb{N}\to X$."
I was under the impression that this is the definition of what it means for a set to be countable and not finite (i.e. "countably infinite"). Then is this a trivial proof, or is it not the true definition and instead the result of a more subtle axiom?
There is a similar question here, but it involves constructing a bijection from $X$ to $\mathbb{N}$ rather than from $\mathbb{N}$ to $X$.