2tuple

A 2tuple, also called a pair or ordered pair, is an ordered collection of two elements. It is typically written as (a, b), where a is the first component and b is the second. A 2tuple belongs to the Cartesian product A × B of two sets A and B, meaning the first element comes from A and the second from B.

In set-theoretic constructions, an ordered pair can be defined to preserve order, such as the Kuratowski definition (a, b) representing the set {{a}, {a, b}}. This formalization ensures that (a, b) ≠ (b, a) unless a = b. By contrast, a set with two elements {a, b} does not retain order and may identify (a, b) with (b, a).

In programming and data representation, 2-tuples appear as pair types or two-field records. They are used to model two related values, such as coordinates or key-value pairs. Different languages provide varying syntax and mutability: for example, tuples in Python are immutable, while records or structs in some languages may be mutable.

Relation to general n-tuples: a 2tuple is the simplest nontrivial n-tuple, and more generally an n-tuple is an element of the Cartesian product A1 × A2 × ... × An. The concept generalizes to many fields, including mathematics, computer science, and databases, where a two-field row or record is a common structural unit.

Examples include (3, "apple"), (x, y), and (5, 5). In a database context, a row with two attributes corresponds to a 2-tuple.