Countable

Definition

A set $A$ is countable if $\mathbb{N} \sim A$. An infinite set that is not countable is called an uncountable set. (Abbott)

A set $X$ is countable if $\# X \leq \#\mathbb{N}$. If $\#\mathbb{N} < \# X$, the set $X$ is said to be uncountable. The cardinality of $\mathbb{N}$ is called $\aleph_{0}$, aleph_null (Schilling).