Introduction: The focus of this study is now directed toward some of the most

fundamental notions of present day mathematics-the notions of sets and operations with sets. The material covered in the preceding section has laid the groundwork for this study by developing the tools of logic needed in the remainder of this text. In fact, many of the results in this chapter closely parallel the corresponding results in Chapter 1. After a foundation is formed with sets, their applications in several areas, such as functions and cardinal numbers, are pursued to provide concepts useful in other areas of mathematics.