# Cartesian product

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## cartesian product

[kär′tē·zhan ′präd·əkt] (mathematics)

In reference to the product of

*P*and*Q,*the set*P*×*Q*of all pairs (*p,q*), where*p*belongs to*P*and*q*belongs to*Q*.## Cartesian product

(mathematics)(After Renee Descartes, French philosper and
mathematician) The Cartesian product of two sets A and B is
the set

A x 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.

See also tuple.

A x B =

**a, b) | a in A, b in**.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.

See also tuple.

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