Book contents
- Frontmatter
- Contents
- NUMBERS: RATIONAL AND IRRATIONAL
- Preface to the Tenth Printing
- Introduction
- Chapter 1 Natural Numbers and Integers
- Chapter 2 Rational Numbers
- Chapter 3 Real Numbers
- Chapter 4 Irrational Numbers
- Chapter 5 Trigonometric and Logarithmic Numbers
- Chapter 6 The Approximation of Irrationals by Rationals
- Chapter 7 The Existence of Transcendental Numbers
- Appendix A Proof That There Are Infinitely Many Prime Numbers
- Appendix B Proof of the Fundamental Theorem of Arithmetic
- Appendix C Cantor's Proof of the Existence of Transcendental Numbers
- Appendix D Trigonometric Numbers
- Answers and Suggestions to Selected Problems
- Index
Preface to the Tenth Printing
- Frontmatter
- Contents
- NUMBERS: RATIONAL AND IRRATIONAL
- Preface to the Tenth Printing
- Introduction
- Chapter 1 Natural Numbers and Integers
- Chapter 2 Rational Numbers
- Chapter 3 Real Numbers
- Chapter 4 Irrational Numbers
- Chapter 5 Trigonometric and Logarithmic Numbers
- Chapter 6 The Approximation of Irrationals by Rationals
- Chapter 7 The Existence of Transcendental Numbers
- Appendix A Proof That There Are Infinitely Many Prime Numbers
- Appendix B Proof of the Fundamental Theorem of Arithmetic
- Appendix C Cantor's Proof of the Existence of Transcendental Numbers
- Appendix D Trigonometric Numbers
- Answers and Suggestions to Selected Problems
- Index
Summary
In the Russian translation of this book published in the U.S.S.R. an additional appendix was added by the mathematician I. M. Yaglom, establishing the irrationality of almost all values of the trigonometric functions for rational degree arguments. It seemed to me that such an appendix should also be included in the English language edition, and I am grateful to Random House for agreeing at once to such an addition. Thus in this printing there is a new Appendix D, TRIGONOMETRIC NUMBERS, establishing the same results as in the Russian version, but with simpler methods I believe. A few minor changes have also been made, mostly clarifications in wording. I am indebted to several correspondents who suggested the improvements.
- Type
- Chapter
- Information
- NumbersRational and Irrational, pp. 2Publisher: Mathematical Association of AmericaPrint publication year: 1961