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.