Unordered pair: Difference between revisions
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In [[axiomatic set theory]], the existence of unordered pairs is required by an axiom, the [[axiom of pairing]]. |
In [[axiomatic set theory]], the existence of unordered pairs is required by an axiom, the [[axiom of pairing]]. |
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==References== |
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* {{Citation | last1=Enderton | first1=Herbert | title=Elements of set theory | publisher=[[Academic Press]] | location=Boston, MA | isbn=978-0-12-238440-0 | year=1977}}. |
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[[Category:Basic concepts in set theory]] |
[[Category:Basic concepts in set theory]] |
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Revision as of 15:57, 26 March 2010
In mathematics, an unordered pair is a set that has exactly two elements. In contrast, an ordered pair consists of a first element and a second element, which need not be distinct. An unordered pair may also be referred to as a two-element set, a pair set, or (rarely) a binary set.
A common notation for unordered pairs is {a,b}, where a and b are the elements of the set. However, if a = b, then {a,b} = {a}, and the set is not an unordered pair but a singleton.
An unordered pair is a finite set; its cardinality (number of elements) is 2.
In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing.
References
- Enderton, Herbert (1977), Elements of set theory, Boston, MA: Academic Press, ISBN 978-0-12-238440-0.