For the following definitions, let be a set, .
A relation on a set is a subset of the Cartesian Product .
An Equivalence Relation on a set is a relation with the following properties:
- Reflexivity: for all .
- Symmetry: .
- Transitivity: and .
Let and be an Equivalence Relation on , then the subset
is an Equivalence Class that is determined by . (Note that contains because .)
Now go lift something heavy,