\begin{definition}[Definition:Associative Operation]
Let $S$ be a set.
Let $\circ : S \times S \to S$ be a binary operation.
Then $\circ$ is '''associative''' {{iff}}:
:$\forall x, y, z \in S: \paren {x \circ y} \circ z = x \circ \paren {y \circ z}$
\end{definition}