Pronunciation: /ɪˈkwɪv ə ləns rɪˈleɪ ʃən/ ?
An equivalence relation is a relationship on a
that shows equality. An example of an equivalence
relation on the set of
is: 5 = 7 + x.
In the table below, R represents the relationship.
Properties of Equivalence Relations
|Property||General Example||Example With Real Numbers||Description|
|Reflexive||a R a||5 = 5||A relationship is reflexive if, for every member a of the set, a R a.|
|Symmetric||a R b implies b R a||If a = b then b = a||A relationship is symmetric if, for every relation a R b on the set, b R a holds.|
|Transitive||a R b and b R c implies a R c||If a = b and b = c, then a = c||A relationship is transitive if, the relationships a R b and b R c imply a R c.|
- equivalence relation. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-25). http://www.merriam-webster.com/dictionary/equivalence relation.
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 7th edition, pp 55-56. Brooks Cole, October 20, 2008.
- R. Hirsch, I. Hodkinson. Relation Algebras by Games, Volume 147 , pg 27. North Holland, August 29, 2002.
- T. S. Blyth, E. F. Robertson. Algebra Through Practice: Volume 1, Sets, Relations and Mappings: A Collection of Problems in Algebra with Solutions, pp 6-14. Cambridge University Press, December 28, 1984.
- McAdams, David. Equal. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Equal.
Cite this article as:
Equivalence Relation. 2010-01-26. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/equivalencerelation.html.
2008-07-26: Added wikipedia to more information (McAdams, David.
2008-04-25: Clarified wording (McAdams, David.
2008-03-31: Initial version (McAdams, David.