ProofWiki:Books/Hermann Weyl/The Continuum: A Critical Examination of the Foundation of Analysis

Hermann Weyl: The Continuum: A Critical Examination of the Foundation of Analysis

Published 1918: Translation 1987 by Stephen Pollard and Thomas Bole, Dover Publications.

ISBN 0-486-67982-9

Subject Matter

• Analysis

Contents

Foreword (by John Archibald Wheeler)

Introduction (by Stephen Pollard)

Preface

Preface to the 1932 Reprint

Chapter 1: Set and Function

Logical Section

$\S 1$. Property, Relation, Existence

$\S 2$. The Principles of the Combination of Judgments

$\S 3$. Logical Inference. Axiomatic Method

Mathematical Section

$\S 4$. Sets

$\S 5$. The Natural Numbers: Richard's Antinomy

$\S 6$. Iteration of the Mathematical Process

The circulus vitiosus of Analysis

$\S 7$. Principles of Substitution & Iteration

$\S 8$. Definitive Formulation of the Foundations.

Introduction of Ideal Elements

Chapter 2: The Concept of Number & The Continuum

$\S 1$. Natural Numbers and Cardinalities

$\S 2$. Fractions and Rational Numbers

$\S 3$. Real Numbers

$\S 4$. Sequences, Convergence Principle

$\S 5$. Continuous Functions

$\S 6$. The Intuitive and The Mathematical Continuum

$\S 7$. Magnitudes and Their Measures

$\S 8$. Curves and Surfaces

Appendix

Notes

Bibliography

Index