Symmetry (of a relation)
From Encyclopedia of Mathematics
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
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