Cartesian product

In mathematics, the Cartesian product (or direct product) of two sets X and Y, denoted X × Y, is the set of all possible ordered pairs whose first component is a member of X and whose second component is a member of Y.

Related Topics:
Mathematics - Set - Ordered pair

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:X × Y = { (x, y) | x ∈ X and y ∈ Y }

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The Cartesian product is named after René Descartes whose formulation of analytic geometry gave rise to this concept.

Related Topics:
René Descartes - Analytic geometry

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For example, if set X is the 13-element set { A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2 } and set Y is the 4-element set {♠, ♥, ♦, ♣}, then the Cartesian product of those two sets is the 52-element set { (A, ♠), (K, ♠), ..., (2, ♠), (A, ♥), ..., (3, ♣), (2, ♣) }.

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