Definition:Countably Infinite Set/Definition 2

Definition
Let $S$ be a set.

$S$ is countably infinite 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.

Also see

 * Equivalence of Definitions of Countably Infinite Set