\begin{definition}[Definition:Commutative/Set]
Let $\struct {S, \circ}$ be an algebraic structure.
Let $X \subseteq S$ be a subset of $S$ such that:
:$\forall a, b \in X: a \circ b = b \circ a$
That is, every element of $X$ commutes with every other element.
Then $X$ is a '''commuting set of elements''' of $S$.
\end{definition}