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Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for anyone wanting to know the answers.
Inhaltsverzeichnis
Introduction; Part I. The Rationals: 1. Counting sheep; 2. The strictly positive rationals; 3. The rational numbers; Part II. The Natural Numbers: 4. The golden key; 5. Modular arithmetic; 6. Axioms for the natural numbers; Part III. The Real Numbers (and the Complex Numbers): 7. What is the problem?; 8. And what is its solution?; 9. The complex numbers; 10. A plethora of polynomials; 11. Can we go further?; Appendix A. Products of many elements; Appendix B. nth complex roots; Appendix C. How do quaternions represent rotations?; Appendix D. Why are the quaternions so special?; References; Index.
Über den Autor / die Autorin
T. W. Körner is Emeritus Professor of Fourier Analysis at the University of Cambridge. His previous books include The Pleasures of Counting (Cambridge, 1996) and Fourier Analysis (Cambridge, 1988).
Zusammenfassung
Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for anyone wanting to know the answers.
