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countable set
Sign in to saveAlso known as at most countable set, enumerable set
set with the same cardinality as some subset of the set of natural numbers
In the Vinony graph
Vinony's link graph records 890 inbound references to countable set, and connects out to bijection, fraction and semantic theory of truth.
Vinony files it under Basic concepts in infinite set theory, Cardinal numbers and Infinity.
Vinony links it to 44 Wikipedia language editions.
Wikidata facts
- Subclass of
- set
Show 5 more facts
- less than
- uncountable set
- different from
- countably infinite set
- Commons category
- Countable sets
- maintained by WikiProject
- WikiProject Mathematics
- studied by
- set theory
via Wikidata · CC0
~22 min read
Encyclopedic overview
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements.
In more technical terms, assuming the axiom of countable choice, a set is countable if its cardinality (the number of elements of the set) is not greater than that of the natural numbers. A countable set that is not finite is said to be countably infinite; for example the set of all natural numbers
Excerpted from Wikipedia’s “countable set” article, available under the CC BY-SA 4.0 licence.