\begin{definition}[Definition:Countable Set/Countably Infinite/Definition 2]
Let $S$ be a set.
$S$ is '''countably infinite''' {{iff}} there exists a bijection:
:$f: S \to \Z$
where $\Z$ is the set of integers.
An infinite set is '''countably infinite''' if it is countable, and is uncountable otherwise.
\end{definition}