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An Introduction to Mathematical Reasoning by Peter J. Eccles

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22

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.

22.1 Partitions

We saw in Chapter 21 that the relation of congruence modulo m partitions the set of integers images into m disjoint ...

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