Adjective
Such that the order in which the operands are taken does not affect their image under the operation.
Usage- not-comparable
- of a binary operation
- Examples
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Addition on the real numbers is commutative because for any real numbers s,t, it is true that s#43;t#61;t#43;s.
Addition and multiplication are commutative operations but subtraction and division are not.
More examples (1)
The associativity of OR and AND is not at all obvious. It is tempting to assume that because OR and AND are commutative that they must be associative also. This is not the case, however, and some commutative Boolean operators are not associative. Examples include NAND and NOR.
Having a commutative operation.
Usage- not-comparable
- of an algebraic structure
Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
Usage- not-comparable
- of a diagram of morphisms
Relating to exchange; interchangeable.
Usage- not-comparable
Adjective
(of a binary operation) independent of order; as in e.g.: ‘a x b’ = ‘b x a’