# Tuple

## 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]