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by H. A. Thurston
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ISBN: 0486458067 Dover Publications Price: $9.95 |
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This book explores arithmetic's underlying concepts and their logical development. It offers an informal and intuitive understanding of the rigorous logical approach, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. Numerous exercises help students test their progress and practice concepts. 1956 edition.
Reprint of the 1967 Dover edition.
Table of Contents for The Number System
| Part I: Explanatory Treatment | |||||||
| 1. Counting | |||||||
| 2. Whole Numbers | |||||||
| 3. The Laws of Arithmetic | |||||||
| 4. Fractions | |||||||
| 5. Negative Numbers | |||||||
| 6. Fields | |||||||
| 7. Irrational Numbers | |||||||
| 8. Powers | |||||||
| 9. Complex Numbers | |||||||
| 10. Verification of the Axioms | |||||||
| 11. Alternative Treatments | |||||||
| Part II: Systematic Treatment | |||||||
| 1. Whole Numbers | |||||||
| 2. Hemigroups and Groups | |||||||
| 3. Integers | |||||||
| 4. Fields | |||||||
| 5. Rational Numbers | |||||||
| 6. Ordered Fields | |||||||
| 7. The Order-Relation for Rationals | |||||||
| 8. Exponentiation | |||||||
| 9. Cauchy Numbers | |||||||
| 10. Real Numbers | |||||||
| 11. Complex Numbers | |||||||
| Bibliography | |||||||
| Key to the Exercises | |||||||
| Index |