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