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# Cartesian product

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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)|(sS) and (tT)}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.

S × T = {(s,t)|(sS) and (tT)}

The concept can be extended to deal with the Cartesian product of n sets,S1,S2,…,SnThis is the set of ordered n-tuples(s1,s2,…,sn)with the property that each si is in Si. In the case where each Si is the same set S, it is customary to write Sn forS × S × … S (n terms)

S1,S2,…,Sn

(s1,s2,…,sn)

S × S × … S (n terms)

Subjects: Computing.

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