Equivalence class

In set theory, an equivalence class is a collection of things that are considered "equal" by some equivalence relation. An equivalence class can be a set or a proper class.

For example, the odd numbers and even numbers are equivalence classes of the integers under the equivalence relation "congruent modulo 2".

Equivalence Class Media

• 

  Congruence is an example of an equivalence relation. The leftmost two triangles are congruent, while the third and fourth triangles are not congruent to any other triangle shown here. Thus, the first two triangles are in the same equivalence class, while the third and fourth triangles are each in their own equivalence class.

• 

  Graph of an example equivalence with 7 classes