Tuple

:For the musical term, see tuplet.

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In mathematics, a tuple is a finite sequence of objects, that is, a list of a limited number of objects (an infinite sequence is a family). Tuples are used to describe mathematical objects that consist of certain components. For example, a directed graph is defined as a tuple (V, E) where V is the set of nodes and E is a subset of V × V that denotes the edges.

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The term originated as an abstraction of the sequence: single, double, triple, quadruple, quintuple, ... n-tuple. A tuple of length n is usually described as an n-tuple. A 2-tuple is an ordered pair; a 3-tuple is a triple or triplet. The n can be any positive integer; thus one can for example say that a quaternion can be represented as a 4-tuple, and further constructed names are possible, such as octuple, but many mathematicians find it quicker to write "8-tuple", even if still pronouncing "octuple".

Finite: In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} where n is a natural number. All finite sets are countable, but not all countable sets are finite....

Sequence: :This is a page about mathematics. For other usages of "sequence", see: sequence (non-mathematical)....

Family: :This article is about the human domestic group. For other uses, see Family (disambiguation)....