Unordered pair

In mathematics, an unordered pair or pair set is a set of the form {"a", "b"}, i.e. a set having two elements "a" and "b" with no particular relation between them, where {"a", "b"} = {"b", "a"}. In contrast, an ordered pair ("a", "b") has "a" as its first element and "b" as its second element, which means ("a", "b") ≠ ("b", "a"). 
While the two elements of an ordered pair ("a", "b") need not be distinct, modern authors only call {"a", "b"} 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 {"a", "a"} 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 (rarely) a binary set.
An unordered pair is a finite set; its cardinality (number of elements) is 2 or (if the two elements are not distinct) 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 {"a"1, "a"2... "an"}.