An equivalence relation on a set 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

1. Reflexive: for all ,

2. Symmetric: implies for all

3. Transitive: and imply for all ,

where these three properties are completely independent. Other notations are often used to indicate a relation, e.g., or .

More things to try:

Weisstein, Eric W. "Equivalence Relation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EquivalenceRelation.html