Definition: Associativity

Let $(X,\ast)$ be an algebraic structure. The binary operation "$\ast$" is called associative if $(x\ast y)\ast z=x\ast (y\ast z)$ holds for any three elements $x,y,z\in X$.

Note: The parentheses in the above definition are a notation of the composition of the function $"\ast$" with itself and it is required that both sides of the following equation are equal:

$$\ast(\ast(x,y),z)=\ast(x,\ast(y,z)).$$