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countable

Definition/Summary
A set is countable if it has the same cardinality as the natural numbers. A set is countable if and only if there is a bijection between the set and the natural numbers.

Equations
The set of integers and rational numbers are countable. The set of all finite subsets of the naturals is countable. The real numbers are not countable.

Every subset of a countable set is countable.

The Cartesian product of finitely many countable sets is countable.

The union of countably many countable sets is countable.

Scientists
Georg Cantor (1845-1918)

Recent forum threads on countable
 
Breakdown
Mathematics
> Foundations
>> Set Theory

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Extended explanation

Commentary

tiny-tim @ 04:00 PM Dec15-09
changed title from "countable set" to "countable" to give more autolinking, since on a forum search the former got 168 hits, and the latter got 500 hits in 3 years.
perhaps needs an explanation of Cantor's diagonal proof, that the real numbers, and the power set of any countable set, are not countable