Each subset induced in a set by a relation of equivalence defined in this set.
Examples
- The relation of congruence modulo n in the set of integers is a relation of equivalence.
- If we group together the elements of E ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} based on the relation R: … has the same remainder as… when we divide by 3, we get three equivalence classes: {1, 4, 7, 10}, {2, 5, 8} and {3, 6, 9}.
- Consider the set of integers that are less than 4 and greater than -4.
Consider the equivalence relation R: … has the same value as … as absolute value.
We get these 4 equivalence classes: {-3, 3}, {-2, 2}, {-1, 1}, {0}.