# Definition:Commutative/Operation

## Definition

Let $\struct {S, \circ}$ be an algebraic structure.

Then $\circ$ is commutative on $S$ if and only if:

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

That is, if every pair of elements of $S$ commutes.

## Historical Note

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.

## Linguistic Note

The word commutative is pronounced with the stress on the second syllable: com-mu-ta-tive.