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.
Then, in 1843, the thought came to him that he could do so if he were willing to abandon the commutative law of multiplication.
Programs work because of the laws of mathematics -- the commutative law for addition, for example -- in the same sense that oil refineries work because of the laws of chemistry.
Generalized commutative laws and generalized associative laws of interval-valued fuzzy soft sets are obtained as well.
Based on these definitions, we can derive the fuzzy versions of familiar properties in ordinary sets, such as commutative laws, deMorgan's laws, etc.