Finite ordered list of elements / From Wikipedia, the free encyclopedia

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In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called respectively a singleton and an ordered pair.

Tuple may be formally defined from ordered pairs by recurrence by starting from ordered pairs; indeed, a n-tuple can be identified with the ordered pair of its (n − 1) first elements and its nth element.

Tuples are usually written by listing the elements within parentheses "( )", separated by a comma and a space; for example, (2, 7, 4, 1, 7) denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "[ ]" or angle brackets "⟨ ⟩". Braces "{ }" are used to specify arrays in some programming languages but not in mathematical expressions, as they are the standard notation for sets. The term tuple can often occur when discussing other mathematical objects, such as vectors.

In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types,[1] tightly associated with algebraic data types, pattern matching, and destructuring assignment.[2] Many programming languages offer an alternative to tuples, known as record types, featuring unordered elements accessed by label.[3] A few programming languages combine ordered tuple product types and unordered record types into a single construct, as in C structs and Haskell records. Relational databases may formally identify their rows (records) as tuples.

Tuples also occur in relational algebra; when programming the semantic web with the Resource Description Framework (RDF); in linguistics;[4] and in philosophy.[5]