Tuple

A tuple is an ordered, finite collection of elements, called components or coordinates, with a fixed length n, where n is a nonnegative integer. An n-tuple is typically written as (a1, a2, ..., an) and is an element of the Cartesian product A1 × A2 × ... × An. The order of elements matters, and two n-tuples are equal if and only if their corresponding components are equal. The 0-tuple, denoted (), is the unique tuple of length zero. In mathematics and computer science, tuples can contain elements of different types.

In computing, a tuple is a finite, ordered collection that is usually immutable and used to group related values. Unlike lists, tuples generally do not support in-place modification after creation. They enable heterogeneous data, such as (name, age, active). Languages vary in syntax and semantics: Python uses parentheses and comma separation to create tuples; many languages treat a 2-tuple as a pair; tuples may be nested and their element types can be fixed or dynamic. Tuples often serve as lightweight records and, if all elements are hashable, can be used as keys in associative structures.

Beyond programming, the term also appears in databases (a row in a relation) and geometry (a point’s coordinates in n-dimensional space). The arity of a tuple is the number of components it contains. In some contexts, a 1-tuple is equivalent to the element itself, which leads to differing conventions. The notion of tuples underpins many formal constructions, including function arguments and product types.