Semigroup

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Demote once it has been fleshed out (to at least in line with monoid)

Note: not to be confused with monoids and groups. Note all groups are monoids and all monoids are semigroups.

Definition

A semigroup is a tuple, $(S,*)$, consisting of a set, $S$ and a binary operation, $*:S\times S\rightarrow S$, where:

• $*$ is associative - $\forall x,y,z\in S[(x*y)*z=x*(y*z)]$