Unordered pair
In mathematics, an unordered pair or pair set is a set of the form, i.e. a set having two elements a and b with no particular relation between them. In contrast, an ordered pair has a as its first element and b as its second element.
While the two elements of an ordered pair need not be distinct, modern authors only call an unordered pair if a ≠ b.
But for a few authors a singleton is also considered an unordered pair, although today, most would say that is a multiset. It is typical to use the term unordered pair even in the situation where the elements a and b could be equal, as long as this equality has not yet been established.
A set with precisely two elements is also called a 2-set or a binary set.
An unordered pair is a finite set; its cardinality is 2 or 1.
In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing.
More generally, an unordered n-tuple is a set of the form.
