# commutative

## English

### Etymology

From French commuter (to substitute or switch) + -ative (tending to). See commute.

commutative (not comparable)

1. () Such that the order in which the operands are taken does not affect their image under the operation.
Addition on the real numbers is commutative because for any real numbers ${\displaystyle s,t}$, it is true that ${\displaystyle s+t=t+s}$.
Addition and multiplication are commutative operations but subtraction and division are not.
2. (algebra, of an algebraic structure) Having a commutative operation.
3. (mathematics, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.

#### Translations

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