Countable Set - Definition

Definition

A set S is called countable if there exists an injective function f from S to the natural numbers

If f is also surjective and therefore bijective (since f is already defined to be injective), then S is called countably infinite.

As noted above, this terminology is not universal: Some authors use countable to mean what is here called "countably infinite," and to not include finite sets.

For alternative (equivalent) formulations of the definition in terms of a bijective function or a surjective function, see the section Formal definition and properties below.

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