Cartesian product

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Revision as of 02:30, 3 November 2008 by imported>Richard Pinch (added para on general index sets)
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In mathematics, the Cartesian product of two sets X and Y is the set of ordered pairs from X and Y. The product of any finite number of sets may be defined inductively.

The product of a general family of sets Xλ as λ ranges over a general index set Λ may be defined as the set of all functions x on Λ such that x(λ) is in Xλ for all λ in Λ. The Axiom of Choice is equivalent to stating that an element of such a product may always be taken.

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