Understanding the infinite /

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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.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lavine, Shaughan
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, Mass. : Harvard University Press, 1998.
Edición:1st Harvard University Press pbk. ed.
Temas:
Mathematics > Philosophy.
Mathématiques > Philosophie.
MATHEMATICS > Set Theory.
PHILOSOPHY > General.
Sets (Mathematics)
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface
  • Contents
  • I. Introduction
  • II. Infinity, Mathematicsâ€? 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 Skolemâ€?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

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