Definition:Commutative

Let $$\circ$$ be a binary operation.

Two elements $$x, y$$ are said to commute (or permute) if $$x \circ y = y \circ x$$.

The binary operation $$\circ$$ is commutative on $$S$$ iff:

$$\forall x, y \in S: x \circ y = y \circ x$$

History
The term "commutative" was coined by François Servois in 1814.

Before this time the commutative nature of addition had been taken for granted since at least as far back as ancient Egypt.