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Semigroup
Set
| context | $S$ |
| definiendum | $ \langle S,* \rangle \in \text{Semigroup}(S)$ |
| postulate | $\langle S,* \rangle\in \mathrm{Magma}(S)$ |
| range | $a,b,c\in S$ |
| postulate | $\forall a,b,c.\ (a*b)*c=a*(b*c)$ |
Discussion
The binary operation is often called multiplication.
The axioms $*\in \mathrm{binaryOp}(S)$ above means that a magma is closed with respect to the multiplication.
One generally calls $S$ the semigroup, i.e. the set where the operation “$*$” is defined on.
Reference
Wikipedia: Semigroup
Subset of
