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The most commonly known examples of associativity are addition and multiplication of natural numbers; for example:
Other examples of associative binary operations include addition and multiplication of real numbers, complex numbers and square matrices; addition of vectors; and intersection and union of sets. Also, if M is some set and S denotes the set of all functions from M to M, then the operation of functional composition on S is associative.
A set with an associative binary operation on it is called a semigroup; monoids and groups are examples of semigroups.
See also Commutativity, Distributive property, Identity element
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