===== Semigroup =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $S$ ... set |
| @#FFBB00: definiendum | @#FFBB00: $\langle\!\langle S,* \rangle\!\rangle \in $ semigroup(S) |
| @#AAFFAA: inclusion   | @#AAFFAA: $\langle\!\langle S,* \rangle\!\rangle\in $ magma(S) |
| @#55EE55: postulate   | @#55EE55: $(a*b)*c=a*(b*c)$ |

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=== 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: 
[[http://en.wikipedia.org/wiki/Semigroup | Semigroup]],
[[https://en.wikipedia.org/wiki/Special_classes_of_semigroups | Special classes of semigroups]]

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=== Subset of ===
[[Magma]]