# N-Tuple

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## N-Tuple

(also ordered *n*-tuple, cortege), in mathematics, an ordered set of *n* elements *(n* is any natural number) called its components or coordinates. Some (or all) components of an *n*-tuple may coincide. Points (vectors) of an *n*-dimensional space are often given in terms of *n*-tuples, namely the ordered sets of their coordinates. Objects that can be described by *n* independent tests are conveniently characterized by means of *n*-tuples.

The concept of an *n* -tuple of numbers plays a fundamental role in the theory of functions of several real variables, and that of an arbitrary *n*-tuple, in linear algebra (the *n*-tuples or vectors of linear algebra are a special case of the more general algebraic concept of a matrix), *n*-tuples are also used, along with other concepts and terms, in mathematical logic, descriptive set theory, topology, functional analysis, the theory of automata, and other branches of mathematics. Basic concepts and formulas of combinatorics are easily and naturally introduced using *n*-tuples.

IU. A. GASTEV