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.
Read more about this topic: Countable Set
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“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
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