The Real Number System in an Algebraic Setting

A grasp of the precision, beauty, and complexity of mathematics requires an understanding of some of the subject's technical aspects. The real number system provides an ideal framework for cultivating such an appreciation, and this detailed investigation of the system offers an accessible introduction. The treatment presumes only a familiarity with the basic properties of natural numbers, although readers must be willing to apply themselves. Proceeding from a review of the natural numbers to the positive rational numbers, the text advances to the nonnegative real numbers and the set of all real numbers.
Author J. B. Roberts stresses self-reliance in this approach, and readers will find that many of the exercises are inseparable from the text and must be completed before moving forward. No proofs are given in the first part of the final chapter, where students are encouraged to use the definitions and theorems to develop the set of all real numbers from the set of nonnegative real numbers. Helpful appendixes introduce cardinal and complex numbers. Suitable as a supplement for any undergraduate course in real numbers, this book is especially valuable for courses in the teaching of mathematics.

Joseph Roberts received his Ph.D. in Mathematics at the University of Minnesota and taught for many years at Reed College in Portland, Oregon, where he is now Professor Emeritus of Mathematics.

I. IntroductionII. The Natural NumbersIII. The Positive Rational NumbersAppendix to Chapter III--Cardinal NumbersIV. Interlude, In Which the Way is Prepared.V. The Nonnegative Real NumbersVI. The Real NumbersAppendix A. Cardinal Numbers.Appendix B. The Complex Numbers.Appendix C. Peano PostulatesAppendix D. Turning an Error to Good Advantage.ReferencesIndex.