Countably Infinite Set has Enumeration

Theorem
Let $S$ be a countably inifnite set.

Then there exists an countably infinite enumeration $\set{s_1, s_2, s_3, \ldots}$ of $S$.

Proof
By definition of countably inifnite set:
 * there exists a bijection $f:S \to \N$

From Inverse of Bijection is Bijection:
 * $f^{-1} : \N \to S$ is a bijection

Let $s = f^{-1}$.

It follows that $s : \N \to S$ is a countably infinite enumeration $\set{s_1, s_2, s_3, \ldots}$ by definition.