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Understanding the infinite /
How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Shaughan Levine attempts to answer this question using a blend of history, philosophy, mathematics and logic.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, Mass. :
Harvard University Press,
1998.
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| Edición: | 1st Harvard University Press pbk. ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface
- Contents
- I. Introduction
- II. Infinity, Mathematics� Persistent Suitor
- 1. Incommensurable Lengths, Irrational Numbers
- 2. Newton and Leibniz
- 3. Go Forward, and Faith Will Come to You
- 4. Vibrating Strings
- 5. Infinity Spurned
- 6. Infinity Embraced
- III. Sets of Points
- 1. Infinite Sizes
- 2. Infinite Orders
- 3. Integration
- 4. Absolute vs. Transfinite
- 5. Paradoxes
- IV. What Are Sets?
- 1. Russell
- 2. Cantor
- 3. Appendix A: Letter from Cantor to Jourdain, 9 July 1904
- 4. Appendix B: On an Elementary Question of Set TheoryV. The Axiomatization of Set Theory
- 1. The Axiom of Choice
- 2. The Axiom of Replacement
- 3. Definiteness and Skolem�s Paradox
- 4. Zermelo
- 5. Go Forward, and Faith Will Come to You
- VI. Knowing the Infinite
- 1. What Do We Know?
- 2. What Can We Know?
- 3. Getting from Here to There
- 4. Appendix
- VII. Leaps of Faith
- 1. Intuition
- 2. Physics
- 3. Modality
- 4. Second-Order Logic
- VIII. From Here to Infinity
- 1. Who Needs Self-Evidence?
- 2. Picturing the Infinite
- 3. The Finite Mathematics of Indefinitely Large Size4. The Theory of Zillions
- IX. Extrapolations
- 1. Natural Models
- 2. Many Models
- 3. One Model or Many? Sets and Classes
- 4. Natural Axioms
- 5. Second Thoughts
- 6. Schematic and Generalizable Variables
- Bibliography
- Index