# Definition:Commutative/Elements

## Definition

Let $\circ$ be a binary operation.

Two elements $x, y$ are said to commute if and only if:

$x \circ y = y \circ x$

Thus $x$ and $y$ can be described as commutative under $\circ$.

## Also known as

The terms permute and permutable can sometimes be seen instead of commute and commutative.

## Also see

• Results about commutativity can be found here.

## 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.