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Let $\circ$ be a binary operation.

Two elements $x, y$ are said to commute (with each other) if and only if:

$x \circ y = y \circ x$

Thus $x$ and $y$ can be described as commutative (elements) 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 Fran├žois 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.