Definition 1.3.1: Equivalence Relation

Let S be a set and r a relation between S and itself. We call r an equivalence relation on S if r has the following three properties:

1. Reflexivity: Every element of S is related to itself
2. Symmetry: If s is related to t then t is related to s
3. Transitivity: If s is related to t and t is related to u, then s is related to u.

Context