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countable (Definition)

A set $S$ is countable if there exists a bijection between $S$ and some subset of $\mathbb{N}$

All finite sets are countable.



"countable" is owned by vampyr.
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See Also: proof that the rationals are countable, Cantor set, average value of function, numerable set


Attachments:
subsets of countable sets are countable (Corollary) by beke
alternative definitions of countable (Definition) by CWoo
product of countable sets (Result) by CWoo
union of countable sets (Result) by CWoo
examples of countable sets (Example) by CWoo
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Cross-references: finite sets, subset, bijection
There are 181 references to this entry.

This is version 2 of countable, born on 2001-11-16, modified 2002-02-27.
Object id is 880, canonical name is Countable.
Accessed 18428 times total.

Classification:
AMS MSC: 03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers)
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flesh out a little? by odenskrigare on 2008-06-05 01:07:19
I guess there's not much else to say here, but I'd like to add that an infinite set in which a finite interval contains a finite number of elements is countable, where an infinite set in which a finite interval contains an infinite amount of elements is uncountable, then give integers vs. reals as an example. I find that definition really useful.
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