Define a semigroup. Give an example of an infinite semigroup.

A semigroup is an algebraic structure consisting of a set \( S \) equipped with an associative binary operation. This means that for all elements \( a, _____ _____ _________ _____ _______ ____ _____ __________ _________.
_______ _______ ____ ________ _______ ________.
___ _________ ________ __________ ________ ________ __________ __________ ________.
___ _____ _________ _____ ________ _______.
_________ _________ ______ __________ ___ ____ _______ ________ ________ __________.
______ ____ _________ ______ _______ ___ _____ _____ _________ ______ ___ ______.
_________ ____ _______ _____ ____ ______ ____ _____ ___ ________.
__________ ____ ______ ________ ___ __________ __________ ______ ___ ________ _____.
______ ______ _______ _________ ____ _________ _______ ____ __________ ___ ______ ____.
______ ________ _____ __________ ________ _______ ____ ____ _________ ______ ______ ________.
__________ _____ ________ __________ _____ __________ _______ ______.
_________ _____ ___ __________ ________.
_______ ____ ________ __________ _______.
______ ________ _______ __________ _______ ________ _______ __________ _________.
____ _____ ____ ________ __________ _____ ________ ______.
___ ________ ____ ___ ___ ______ _______ __________.
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