# Tuple

In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an (ordered) -tuple is a sequence (or ordered list) of elements, where is a positive integer. One 0-tuple, an empty sequence, also exists. An -tuple is defined inductively using the construction of an ordered pair. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple. Sometimes other delimiters are used, like square brackets "" or angle brackets "". Braces "" are almost never used for tuples, since they are the standard notation for sets.

Tuples are often used for describing other mathematical objects, like vectors. In algebra, a ring is commonly defined a 3-tuple, where is some set, and "", and "" are functions mapping the Cartesian product to with specific properties. The Informatics implementation of tuples is product types in most functional programming languages. The rather common implementation of tuples is record types, where the components are labeled instead of being identified by position alone. This approach is also used in relational algebra.