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.^{[1]}^{[2]}^{[3]}^{[4]} 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 2set 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 ntuple is a set of the form {a_{1}, a_{2},... a_{n}}.^{[5]}^{[6]}^{[7]}
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Introduction to Combinations (Unordered Selections)

Lecture: Unordered sampling without replacement

Ordered pair Meaning
Transcription
Notes
 ^ Düntsch, Ivo; Gediga, Günther (2000), Sets, Relations, Functions, Primers Series, Methodos, ISBN 9781903280003.
 ^ Fraenkel, Adolf (1928), Einleitung in die Mengenlehre, Berlin, New York: SpringerVerlag
 ^ Roitman, Judith (1990), Introduction to modern set theory, New York: John Wiley & Sons, ISBN 9780471635192.
 ^ Schimmerling, Ernest (2008), Undergraduate set theory
 ^ Hrbacek, Karel; Jech, Thomas (1999), Introduction to set theory (3rd ed.), New York: Dekker, ISBN 9780824779153.
 ^ Rubin, Jean E. (1967), Set theory for the mathematician, HoldenDay
 ^ Takeuti, Gaisi; Zaring, Wilson M. (1971), Introduction to axiomatic set theory, Graduate Texts in Mathematics, Berlin, New York: SpringerVerlag
References
 Enderton, Herbert (1977), Elements of set theory, Boston, MA: Academic Press, ISBN 9780122384400.