Monoid
A monoid is a set that is closed under an associative binary operation and has an identity
element 
such that for all 
, 
. Note that
unlike a group, its elements need not have inverses. It
can also be thought of as a semigroup with an identity
element.
A monoid must contain at least one element.
A monoid that is commutative is, not surprisingly, known as a commutative monoid.
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