Aside on equivalence relations
A relation on a set is a subset of . By a slight abuse of notation, let us write, for any , if and only if . An equivalence relation is a relation satisfying (for equivalence relations, we write instead of )
- for all , (reflexive),
- for all , implies (symmetric),
- for all , if and then (transitivity).
The equivalence class of is
If is an equivalence class of then we call (or any other element of ) a representative of in .
David Joyner 2007-09-03