N-tuple

A tuple is a finite ordered list of elements. In mathematics, an $n$ -tuple is a sequence (or ordered list) of $n$ elements, where $n$ is a non-negative integer. There is only one 0-tuple, an empty sequence. An $n$ -tuple is defined inductively using the construction of an ordered pair. Tuples are usually written by listing the elements within parentheses " $({\text{ }})$ $(\text{ })$ " and separated by commas; for example, $(2,7,4,1,7)$ $(2, 7, 4, 1, 7)$ denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "[ ]" or angle brackets "< >". Braces "{ }" are only used in defining arrays in some programming languages such as Java, but not in mathematical expressions, as they are the standard notation for sets. Tuples are often used to describe other mathematical objects, such as vectors. In computer science, tuples are directly implemented as product types in most functional programming languages. More commonly, they are implemented as record types, where the components are labeled instead of being identified by position alone. This approach is also used in relational algebra. Tuples are also used in relation to programming the semantic web with the Resource Description Framework (RDF). Tuples are also used in linguistics and philosophy.

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