Countable

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Countable refers to something that may be counted. For example, it may refer to a group of items that may be separated into individual components.

Formally we say that a set $S$ is countably infinite if and only if there exists a one-to-one correspondence (bijection) between $S$ and $\mathbb{N}$, the set of natural numbers. A set is countable if it is either finite or countably infinite.

The definition may also be formulated as: a set $S$ is countable is there exists an injection from $S$ to $\mathbb{N}$, or if there exists a surjection from $\mathbb{N}$ to $S$.

See also

• Natural number