3tuple

A 3-tuple, also known as a triple, is an ordered triple of three elements. In mathematics and computer science, a k-tuple is a sequence of k elements, where the order of elements is significant. A 3-tuple is written as (a, b, c) and is an element of the Cartesian product A × B × C, with a ∈ A, b ∈ B, c ∈ C.

Properties: The components can be any objects; repetition is allowed; two 3-tuples are equal if and only if their corresponding components are equal. The length is fixed, and a 3-tuple can be projected to its components using projection functions π1, π2, π3 that retrieve a, b, and c respectively.

In practical terms, 3-tuples model simple records or coordinates. Common uses include representing a point in three-dimensional space (x, y, z) or a color in RGB space (r, g, b). In programming languages, 3-tuples often serve as lightweight data containers with fixed arity and may be immutable.

Examples across languages: in Python, t = (3, 'red', True) creates a three-element tuple; t[0] yields 3. In Haskell, a triple is written as (a, b, c) with type (a, b, c). In databases, a row can be viewed as a tuple of three fields, though rows are usually longer and named by column.

Related concepts include n-tuples, Cartesian products, and vectors. The 3-tuple is a fundamental construct for organizing a fixed-length collection of related values in both mathematics and computing.