Unordered pair: Difference between revisions

Content deleted Content added

Inline

Revision as of 16:56, 3 April 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.

@@ Line 1: / Line 1: @@
 In [[mathematics]], an '''unordered pair''' is a [[Set (mathematics)|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''&nbsp;=&nbsp;''b'', then {''a'',''b''}&nbsp;=&nbsp;{''a''}, and the set is not an unordered pair but a [[singleton (mathematics)|singleton]].
+A common notation for unordered pairs is {''a'',&nbsp;''b''}, where ''a'' and ''b'' are the elements of the set. However, if ''a''&nbsp;=&nbsp;''b'', then {''a'',&nbsp;''b''}&nbsp;=&nbsp;{''a''}, and the set is not an unordered pair but a [[singleton (mathematics)|singleton]].
 An unordered pair is a [[finite set]]; its [[cardinality]] (number of elements) is&nbsp;2.