Partitions and equivalence relations
In the previous chapter we saw that congruence of integers can be viewed in two ways: as a relation between certain integers and as a partition of the set of integers. This is an example of a very general concept, known as an equivalence relation, which the reader will encounter frequently in more advanced pure mathematics.
An equivalence relation on a set corresponds to a partition of the set. In this chapter this correspondence is explained and a number of examples discussed.
We saw in Chapter 21 that the relation of congruence modulo m partitions the set of integers into m disjoint ...