Binary operation/Neutral element/Definition

Let a set ${\displaystyle {}M}$ and a binary operation

${\displaystyle \circ \colon M\times M\longrightarrow M,(x,y)\longmapsto x\circ y,}$

be given. An element ${\displaystyle {}e\in M}$ is called neutral element of the operation if, for all ${\displaystyle {}x\in M}$, the equalities ${\displaystyle {}x\circ e=x=e\circ x}$ hold.