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countably infinite (Definition)

A set $ S$ is countably infinite if there is a bijection between $ S$ and $ \mathbb{N}$.

As the name implies, any countably infinite set is both countable and infinite.

Countably infinite sets are also sometimes called denumerable.



"countably infinite" is owned by vampyr.
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See Also: numerable set

Other names:  denumerable
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Cross-references: infinite, countable, implies, bijection
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This is version 3 of countably infinite, born on 2001-11-16, modified 2002-06-14.
Object id is 883, canonical name is CountablyInfinite.
Accessed 9616 times total.

Classification:
AMS MSC: 03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers)
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