Equivalence relation

In mathematics, an equivalence relation on a set X is a binary relation on X that is reflexive, symmetric and transitive, i.e., if the relation is written as ~ it holds for all a, b and c in X that

Related Topics:
Mathematics - Set - Binary relation

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• (Reflexivity) a ~ a
• (Symmetry) if a ~ b then b ~ a
• (Transitivity) if a ~ b and b ~ c then a ~ c

A set together with an equivalence relation is called a setoid.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Equivalence relations are often used to group together objects that are similar in some sense.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

 
Equivalence relation: Examples of equivalence relations ►