# Cartesian product

- The Cartesian product of two sets, A and B (written A × B), is the set of all ordered pairs whose first member is an element of A, and whose second member is an element of B.

*Philosophy dictionary.
Academic.
2011.*

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**Cartesian product**— Cartesian square redirects here. For Cartesian squares in category theory, see Cartesian square (category theory). In mathematics, a Cartesian product (or product set) is a construction to build a new set out of a number of given sets. Each… … Wikipedia**Cartesian product**— noun The set of all possible pairs of elements whose components are members of two sets. Notation: . Syn: direct product … Wiktionary**Cartesian product**— noun the set of elements common to two or more sets the set of red hats is the intersection of the set of hats and the set of red things • Syn: ↑intersection, ↑product • Hypernyms: ↑set … Useful english dictionary**Cartesian product**— noun Date: 1958 a set that is constructed from two given sets and comprises all pairs of elements such that the first element of the pair is from the first set and the second is from the second set … New Collegiate Dictionary**Cartesian product**— Math. the collection of all ordered pairs of two given sets such that the first elements of the pairs are chosen from one set and the second elements from the other set: this procedure generalizes to an infinite number of sets. [1955 60] * * * … Universalium**Cartesian product of graphs**— In graph theory, the cartesian product G ◻ H of graphs G and H is a graph such that * the vertex set of G ◻ H is the cartesian product V(G) × V(H) ; and * any two vertices (u,u ) and (v,v ) are adjacent in G ◻ H if and only if either ** u = v and … Wikipedia**Cartesian**— means of or relating to the French philosopher and mathematician René Descartes mdash; from his name mdash; Rene Des Cartes .See:*Cartesian dualism * Cartesian Meditations , a work by Edmund Husserl * Cartesian linguistics , a work by Noam… … Wikipedia**Cartesian set**— Cartesian product or Cartesian set, Mathematics. the set of all ordered pairs that can be formed by matching each member of one set with each member of a second set in turn … Useful english dictionary**Cartesian closed category**— In category theory, a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in… … Wikipedia**Product (category theory)**— In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct… … Wikipedia