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    Commutativity

    Alternate names

    commutative property | commutativity | law of commutativity

    Basic definition

    An operation * is said to be commutative if x*y = y*x for all x and y.

    Detailed definition

    Two elements x and y of a set S are said to be commutative under a binary operation * if they satisfy x*y = y*x. Real numbers are commutative under addition x + y = y + x and multiplication x·y = y·x. The Wolfram Language attribute that sets a function to be commutative is Orderless.

    Related terms

    associative | commutative algebra | commutative diagram | commutative monoid | commutative ring | commute | commuting matrices | distributive | transitive

    Related Wolfram Language symbol

    Orderless

    Educational grade level

    elementary school level (California grade 2 standard)

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