commutative law

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commutative law

commutative law in mathematics, law holding that for a given binary operation (combining two quantities) the order of the quantities is arbitrary; e.g., in addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7. More generally, in addition, for any two numbers a and b the commutative law is expressed as a + b = b + a. Multiplication of numbers is also commutative, i.e., a × b = b × a. In general, any binary operation, symbolized by [symbol], joining mathematical entities A and B obeys the commutative law if A [symbol] B = B [symbol] A for all possible choices of A and B. Not all operations are commutative; e.g., subtraction is not since 2-5≠5-2, and division is not since 2/5 ≠ 5/2 .

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commutative law

World Encyclopedia | 2005 | Â© World Encyclopedia 2005, originally published by Oxford University Press 2005. (Hide copyright information) Copyright

commutative law Rule of combination in mathematics; it requires that an operation on two terms is independent of the order of the terms. Addition and multiplication of numbers is commutative, since a + b = b + a and ab = ba. Vector cross-multiplication does not obey the commutative law.

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