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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