Cover: Understanding the Infinite, from Harvard University PressCover: Understanding the Infinite in PAPERBACK

Understanding the Infinite

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Product Details

PAPERBACK

$41.00 • £32.95 • €37.00

ISBN 9780674921177

Publication Date: 01/13/1998

Short

376 pages

6-3/8 x 9-1/4 inches

3 line illustrations

World

  • 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
    • Appendix: Letter from Cantor to Jourdain, 9 July 1904
    • Appendix: On an Elementary Question of Set Theory
  • V. 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
    • 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 Size
    • 4. 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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