Monoid
Set
| context | $M$ … set |
| definiendum | $ \langle\!\langle M,*\rangle\!\rangle \in$ it |
| inclusion | $*$ … binary operation |
| exists | $e$ |
| postulate | $e$ … unit element $\langle\!\langle M,*\rangle\!\rangle$ |
| postulate | $(a*b)*c=a*(b*c)$ |
Discussion
The binary operation is often called multiplication and $e$ is called the identity, identity element or unit.
One generally calls $M$ the monoid, i.e. the set where the operation “$*$” is defined on, not the pair. For example, not that “A monoid is non-empty”.
Like above, one often uses infix notion for $*$.
Reference
Wikipedia: Monoid
Requirements
Subset of
