# Cartesian product

## Cartesian product

noun Mathematics.
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.

Origin:
1955–60

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 Cartesian product —n maths, logic Also called: cross product the set of all ordered pairs of members of two given sets. The product A × B is the set of all pairs where a is a member of A and b is a member of B

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### Cartesian product definition

mathematics
(After Renee Descartes, French philosper and mathematician) The Cartesian product of two sets A and B is the set
A x B = (a, b) | a in A, b in B.
I.e. the product set contains all possible combinations of one element from each set. The idea can be extended to products of any number of sets.
If we consider the elements in sets A and B as points along perpendicular axes in a two-dimensional space then the elements of the product are the "Cartesian coordinates" of points in that space.