Countable Set

Let $X$ be a set and let $\mathbb{N}$ be the set of natural numbers.

The set $X$ is countable if $X$ is empty, or there is a sequence $(x_{n})_{n\in\mathbb{N}}$ in $X$ whose set of terms is $X$, meaning that for every $y\in X$ there is $n\in\mathbb{N}$ with $y=x_{n}$.