ThmDex – An index of mathematical definitions, results, and conjectures.

Formulation F3291 on D265: Monoid

F3291

Formulation 0

A D263: Groupoid $G = (X, +)$ is a monoid if and only if

(1)	\begin{equation} \forall \, x, y, z \in X : (x + y) + z = x + (y + z) \end{equation}
(2)	\begin{equation} \exists \, 0_G \in X : \forall \, x \in X : 0_G + x = x + 0_G = x \end{equation}