Set Theory

Very often, these computations involve collections of data, for example, a class management system might store a collection of students, or a server might need to track the set of computers it can directly communicate with on the network. Furthermore, these computations can frequently be phrased in terms of manipulations of or queries over these data, for example, generating pairs of students for a class activity, or finding if there exists a series of computers that connect the server to some other computer on the network. To model this, we often utilize mathematical sets. A set is a collection of distinct objects, i.e., there are no duplicates in a set. Set theory is the branch of mathematics that studies how we construct and manipulate sets. Because virtually any mathematical model includes data of some sort, whether they are integers, real numbers, or more abstract objects, sets form the basis of formal mathematics. In addition to using sets directly in our models, we’ll also see sets in every other mathematical In this chapter, we briefly explore the field of set theory with an eye towards building up a working understanding of what set theory provides us and what questions we can answer by framing our problems in terms of sets.