Countable Set

Definite

$X$ is finite or $|X|=|\mathbb{N}|$

A set is finite or there exists an Injective function from it into the natural numbers

Facts

A subset of a countable set is countable

Any finite union of countable set is countable

$\mathbb{N}\times \mathbb{N}$ is countable

The Cartesian Product of finitely many countable sets is countable

$\mathbb{Z}$ and $\mathbb{Q}$ are countable