## Semigroup

### Set

 context $S$ … set definiendum $\langle\!\langle S,* \rangle\!\rangle \in$ semigroup(S) inclusion $\langle\!\langle S,* \rangle\!\rangle\in$ magma(S) postulate $(a*b)*c=a*(b*c)$

#### 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.