Equivalence class ↩

Metadata

aliases: []
shorthands: {}
created: 2021-11-14 20:23:22
modified: 2022-01-10 04:13:04

Let

be a set and

be an equivalence relation on

. Then the equivalence class of an element

is the following:

Other notation:

It can be shown from the properties of equivalence relations that the equivalence classes form a partition on the set. This means that the equivalence classes are disjoint subsets of while covering the whole set.