Cartesian product

A Dictionary of Computing | 2004 | 700+ words | Copyright

Cartesian product of two sets S and T. The set of all ordered pairs of the form (s,t) with the property that s is a member of S and t is a member of T; this is usually written as S × T. Formally, S × T = {(s,t)|(s ∈ S) and (t ∈ T)}

If R denotes the set of real numbers, then R × R is just the set of points in the (Cartesian) plane or it can be regarded as the set of complex numbers, hence the name.

The concept can be extended to deal with the Cartesian product of n sets, S₁,S₂,…,S_n

This is the set of ordered n-tuples (s₁,s₂,…,s_n)

with the property that each s_i is in S_i. In the case where each S_i is the same set S, it is customary to write Sⁿ for S × S × … S (n terms)

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JOHN DAINTITH. "Cartesian product." A Dictionary of Computing. 2004. Encyclopedia.com. 27 May. 2012 <http://www.encyclopedia.com>.

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