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

A semigroup is a set equipped with a binary operation that is associative. This means that for any three elements aa, bb, and cc in the semigroup, the operation satisfies the condition (a⋅b)⋅c=a⋅(b⋅c)(a \cdot b) \cdot _____ ____ ______ __________ _______ _______ ____ ___ ____.
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