The Real Number System

  • ISBN13:


  • ISBN10:


  • Edition: Reprint
  • Format: Paperback
  • Copyright: 2018-09-12
  • Publisher: Dover Publications
  • Purchase Benefits
  • Free Shipping Icon Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • eCampus.com Logo Get Rewarded for Ordering Your Textbooks! Enroll Now
List Price: $14.95 Save up to $0.75
  • Buy New


Supplemental Materials

What is included with this book?


Concise but thorough and systematic, this categorical discussion of the real number system presents a series of step-by-step axioms, each illustrated by examples. The highly accessible text is suitable for readers at varying levels of knowledge and experience: advanced high school students and college undergraduates as well as prospective high school and college instructors. The abundance of examples and the wealth of exercises—more than 300, all with answers provided—make this a particularly valuable book for self-study.
The first two chapters examine fields and ordered fields, followed by an introduction to natural numbers and mathematical induction. Subsequent chapters explore composite and prime numbers, integers and rational numbers, congruences and finite fields, and polynomials and rational functions. Additional topics include intervals and absolute value, the axiom of completeness, roots and rational exponents, exponents and logarithms, and decimal expansions. A helpful Appendix concludes the text.

Author Biography

John M. H. Olmsted was Professor of Mathematics at Southern Illinois University in Carbondale, Illinois. He also wrote books on calculus, and Dover publishes his Counterexamples in Analysis, co-written with Bernard R. Gelbaum.

Table of Contents

1. Fields
2. Ordered Fields
3. Natural Numbers and Mathematical Induction 
4. Composite and Prime Numbers
5. Integers and Rational Numbers
6. Congruences and Finite Fields
7. Polynomials and Rational Functions
8. Intervals and Absolute Value
9. The Axiom of Completeness
10. Roots and Rational Exponents
11. Exponents and Logarithms
12. Decimal Expansions
Answers to Problems
List of Special Symbols

Rewards Program

Reviews for The Real Number System (9780486827643)