The difference between Monoid and Semigroup
When used as nouns, monoid means a set which is closed under an associative binary operation, and which contains an element which is an identity for the operation, whereas semigroup means any set for which there is a binary operation that is closed and associative.
Monoid is also adjective with the meaning: containing only one kind of metrical foot.
check bellow for the other definitions of Monoid and Semigroup
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Monoid as a noun (mathematics):
A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
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Monoid as an adjective (prosody):
Containing only one kind of metrical foot.
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Semigroup as a noun (mathematics):
Any set for which there is a binary operation that is closed and associative.