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Associative property

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A binary operation * on a set S is associative if, for all x, y and z in S, (x * y) * z  =  x * (y * z).

Examples of associative binary operations include addition and multiplication of complex numbers, addition of vectors, and intersection and union of sets.

A set with an associative binary operation on it is called a semigroup.

See also Commutative.

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