• Provides a careful development of the real number system which lays the foundation for abstract algebra, number theory, and analysis.
• The methods of correct proof writing are emphasized.
• The exercises at the end of each section are designed to further the student’s understanding of the material and to assist in the student’s development of proof writing.
• Teaches students how to understand and construct proofs of theorems that possess important mathematical content.
• Many of the steps taken in the development of the real number system demonstrate techniques and strategies that will be used time and time again in the student’s mathematics career.
• The approach assists the student in integrating his/her everyday experience with real numbers to the theory of real numbers.

Chapter 1. Logic and Techniques For Proofs                                                            

Chapter 2. Elementary Set Theory                                                                                  

Chapter 3. The Development of the Integers                                                                          

Chapter 4. Properties and Applications of Integers

Chapter 5. Fields and the Rational Numbers

Chapter 6. The Development of the Real Numbers

Chapter 7. Some Additional Properties of Real Numbers

Appendix A: Proof of the Cantor-Schroder-Bernstein Theorem

Appendix B: Using the Axiom of Choice to Prove Some Results About Infinite Sets

Appendix C: Completion of the Construction of a Set Obeying the Real Number Postulates

References