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by Friedrich Waismann
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ISBN: 0486428044 Dover Publications Price: $14.95 |
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Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; and more. Includes 27 figures. Index. 1959 edition.
Unabridged republication of the edition published by Harper & Row, New York, 1959.
Table of Contents for Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics
| Foreward | |||||||
| Author's Preface | |||||||
| 1. The Various Types of Numbers | |||||||
| 2. Criticism of the Extension of Numbers | |||||||
| 3. Arithmetic and Geometry | |||||||
| 4. The Rigorous Construction of the Theory of Integers | |||||||
| 5. The Rational Numbers | |||||||
| 6. Foundation of the Arithmetic of Natural Numbers | |||||||
| 7. Rigorous Construction of Elementary Arithmetic | |||||||
| 8. The Principle of Complete Induction | |||||||
| 9. Present Status of the Investigation of the Foundations | |||||||
| A. Formalism | |||||||
| B. The Logical School | |||||||
| C. Outlook | |||||||
| 10. Limit and Point of Accumulation | |||||||
| 11. Operating with Sequences. Differential Quotient | |||||||
| 12. Remarkable Curves | |||||||
| Appendix: What is Geometry? | |||||||
| 13. The Real Numbers | |||||||
| A. Cantor's Theory | |||||||
| B. Dedekind's Theory | |||||||
| C. Comparison of the Two Theories | |||||||
| D. Uniqueness of the Real Number System | |||||||
| E. Various Remarks | |||||||
| 14. Ultrareal Numbers | |||||||
| 15. Complex and Hypercomplex Numbers | |||||||
| 16. Inventing or Discovering | |||||||
| Epilogue | |||||||
| Index |