Namespaces
Variants
Actions

Symmetry (of a relation)

From Encyclopedia of Mathematics
Revision as of 17:16, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A property of a binary relation. A binary relation on a set is called symmetric if for any pair of elements , implies , i.e. . An example of a symmetric relation is an equivalence.


Comments

An anti-symmetric relation on a set is a reflexive relation such that .

References

[a1] P.M. Cohn, "Algebra" , 1 , Wiley (1982) pp. 17ff
How to Cite This Entry:
Symmetry (of a relation). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Symmetry_(of_a_relation)&oldid=33590
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article