An equivalence relation on a set subset of ordered pairs of elements
of element of
1. Reflexive : for all
2. Symmetric : implies for all
3. Transitive : imply for all
where these three properties are completely independent. Other notations are often used to indicate a relation , e.g.,
See also Algebra Congruence ,
Equivalence
Class ,
Teichmüller Space
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References Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Stewart, I. and Tall, D. The
Foundations of Mathematics. Referenced
on Wolfram|Alpha Equivalence Relation
Cite this as:
Weisstein, Eric W. "Equivalence Relation."
From MathWorld https://mathworld.wolfram.com/EquivalenceRelation.html
Subject classifications
is a subset of 
, i.e., a collection 
of ordered pairs of elements
of 
,
satisfying certain properties. Write "
" to mean 
is an element of 
, and we say "
is related to 
," then the properties are
,
implies 
for all 
,
and 
imply 
for all 
,
or 
.
