Cartesian product

For any sets A and B, the Cartesian product A×B is the set consisting of all ordered pairs (a,b) where aA and bB.

The Cartesian product satisfies the following properties, for all sets A, B, C, and D:

  • A×=

  • (A×B)(C×D)=(AC)×(BD)

  • (A×B)=(A×B)(A×B)(A×B)

Here denotes the empty setMathworldPlanetmath, denotes intersectionMathworldPlanetmath, denotes union, and denotes complement with respect to some universal set U containing A and B.

Title Cartesian product
Canonical name CartesianProduct
Date of creation 2013-03-22 11:48:56
Last modified on 2013-03-22 11:48:56
Owner djao (24)
Last modified by djao (24)
Numerical id 10
Author djao (24)
Entry type Definition
Classification msc 03-00
Classification msc 81P10
Classification msc 81P05
Related topic GeneralizedCartesianProduct