An equivalence relation is a binary Relation, $R$ on a Set $X$ that satisfies:

• Reflexivity
• Symmetry
• Transitivity

The set of elements which are all related by an equivalence relation is called an Equivalence class. The collection of equivalence classes of a set with an equivalence relation produces a Partition (vid).

We often can define structures/operations on equivalence classes by defining it in representatives of the classes. This is only well defined if the definition is independent of the choice of represenatative

Review of equivalence relations