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

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