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( Countable set)
In mathematics, a countable set is a set with the same cardinality (i.e., number of elements) as some subset of the set of natural numbers. The term was originated by Georg Cantor; it stems from the fact that the natural numbers are often called counting numbers. A set that is not countable is called uncountable. Some authors use countable set to mean a set with exactly as many elements as the set of natural numbers. The difference between the two definitions is that under the former, finite sets are also considered to be countable, while under the latter definition, they are not considered to be countable. To resolve this ambiguity, the term at most countable is sometimes used for the former notion, and countably infinite for the latter. A set S is called countable if there exists an injective function If f is also surjective, thus making f bijective, then S is called countably infinite or denumerable.
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