| Share

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 ∘, joining mathematical entities A and B obeys the commutative law if AB = BA 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.

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

More on commutative law from Infoplease:

See more Encyclopedia articles on: Mathematics

Premium Partner Content
HighBeam Research
Documents Images and Maps Reference
(from Newspapers, Magazines, Journals, Newswires, Transcripts and Books)

Research our extensive archive of more than 80 million articles from 6,500 publications.

Additional search results provided by HighBeam Research, LLC. © Copyright 2005. All rights reserved.

24 X 7

Private Tutor

Click Here for Details
24 x 7 Tutor Availability
Unlimited Online Tutoring
1-on-1 Tutoring