Binary operation/Associative/Definition

A binary operation

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

on a set ${\displaystyle {}M}$ is called associative if for all ${\displaystyle {}x,y,z\in M}$ the equality

${\displaystyle {}(x\circ y)\circ z=y\circ (x\circ z)\,}$

holds.