Sets, Maps, and Relations

Abstract

There are two main languages in which theoretical computer science is expressed — the language of sets and the language of numbers. The principal aim of this chapter is to set forth the basic concepts of set theory. Section 1.1 introduces sets and subsets, and shows how to build up new sets from old ones by such operations as the Cartesian product, union, intersection, and set differences. Section 1.2 briefly summarizes fundamental facts about exponents, logarithms, and finite series. Section 1.3 introduces the basic notions of maps or functions, partial functions, and relations. The way in which computer programs transform input data provides examples of partial functions. Finding relations between items stored in a data base is an important task for computer science.