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

  1. 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=.
  2. 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.
  3. 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.

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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.)

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