chapter  13
10 Pages

Partitions

In the last chapter we dealt with relations and in particular the important category of relations called equivalence relations. A concept closely related to this is the concept of partitions. A partitioning of a set A is accomplished by subdividing A into categories so that each of its members is in one, and only one, category. A partitioning of the students at a university occurs, for example, by dividing them into academic classes: freshmen, sophomores, juniors, seniors, and graduate students. Neglecting exceptional cases, every student is in one of these categories and no student is in more than one. From this, it is easy to formalize the concept into a definition.