Sets and Mappings

In this chapter you will learn some of the basic ideas of set theory, particularly those associated with mappings or functions. These will be used extensively in the following chapters and, indeed, in all of mathematics. This is not a systematic treatment of set theory. It omits many essential ideas, such as, infinity, cardinal and ordinal numbers, and foundational problems, that are not directly needed in this book. I assume that you have had some experience with the use of sets, so I do not give many examples of the familiar terms. Of course, you should not look in other books to find proofs of the theorems and the exercises of this chapter, because that would defeat the purpose of the book. However, if you want to see further discussion of the topics taken up here, you can look at books in set theory.