Associative
Pronunciation: /əˈsoʊ siˌeɪ tɪv/ ?
A binary operation
'*' is associative if, for all values of
a, b, and
c; a * (b * c) = (a * b) * c.^{[1]}
Some binary operations that are associative are:
- Addition: a + (b + c) = (a + b) + c.
- Multiplication: a(bc) = (ab)c.
A binary operation that is not associative is:
- Subtraction: a - (b - c) ≠ (a - b) - c.
References
- associative. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=associative&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
- Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically, 2nd edition, pg 5. D. C. Heath & Co., Boston, U.S.A., 1907. (Accessed: 2009-12-19). http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n14/mode/1up/search/associative.
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 28-29. Thomson, Brooks/Cole, 2005.
More Information
- McAdams, David. Associative Property of Addition. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Associative Property of Addition.
- McAdams, David. Associative Property of Multiplication. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Associative Property of Multiplication.
Cite this article as:
Associative. 2010-01-07. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/associative.html.
Translations
Image Credits
Revision History
2010-01-07: Added "References" (
McAdams, David.)
2008-04-24: Added 'Associative Property of Multiplication' to More Information (
McAdams, David.)
2008-04-22: Initial version (
McAdams, David.)