commutative law


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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 +, joining mathematical entities A and B obeys the commutative law if A+B=B+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.

commutative law

[¦käm·yə‚tād·iv ‚lȯ]
(mathematics)
A rule which requires that the result of a binary operation be independent of order; that is, ab = ba.
References in periodicals archive ?
Knowledge of the commutative law necessitates exposure to subtractions with a negative result and divisions with a result that is less than one.
the commutative law for the preceding union definition holds as A [intersection] B = B [intersection] A).
Then, in 1843, the thought came to him that he could do so if he were willing to abandon the commutative law of multiplication.