The Continuum: A Critical Examination of the Foundation of Analysis

Overview

This classic text deals with the conceptual problem posed by the continuum — the set of all real numbers. Chapter 1 deals with the logic and mathematics of set and function, while Chapter 2 focuses on the concept of number and the continuum. Advanced-level mathematical landmark will interest anyone working in foundational analysis. Bibliography. Originally published 1918.

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Overview

This classic text deals with the conceptual problem posed by the continuum — the set of all real numbers. Chapter 1 deals with the logic and mathematics of set and function, while Chapter 2 focuses on the concept of number and the continuum. Advanced-level mathematical landmark will interest anyone working in foundational analysis. Bibliography. Originally published 1918.

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Product Details

  • ISBN-13: 9780486679822
  • Publisher: Dover Publications
  • Publication date: 3/14/1994
  • Series: Dover Books on Mathematics Series
  • Edition description: Reprint
  • Pages: 176
  • Sales rank: 837,758
  • Product dimensions: 5.39 (w) x 8.48 (h) x 0.37 (d)

Meet the Author

Along with his fundamental contributions to most branches of mathematics, Hermann Weyl (1885-1955) took a serious interest in theoretical physics. In addition to teaching in Zürich, Göttingen, and Princeton, Weyl worked with Einstein on relativity theory at the Institute for Advanced Studies.

Hermann Weyl: The Search for Beautiful Truths
One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885–1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years.

In the Author's Own Words:
"My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."

"We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context."

"A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." — Hermann Weyl

Critical Acclaim for Space, Time, Matter:
"A classic of physics . . . the first systematic presentation of Einstein's theory of relativity." — British Journal for Philosophy and Science

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Table of Contents

Foreword; Introduction; Preface
Chapter 1. Set and Function
  Logical Section
  1. Property, Relation, Existence
  2. The Principles of the combination of Judgments
  3. Logical Inference. Axiomatic Method
  Mathematical Section
  4. Sets
  5. The Natural Numbers: Richard's Antinomy
  6. Iteration of the Mathematical Process. The circulus vitiosus of Analysis
  7. Principles of Substitution & Iteration
  8. Definitive Formulation of the Foundations. Introduction of Ideal Elements
Chapter 2. The Concept of Number & The Continuum
  1. Natural Numbers and Cardinalities
  2. Fractions and Rational Numbers
  3. Real Numbers
  4. Sequences, Convergence Principle
  5. Continuous Functions
  6. The Intuitive and the Mathematical Continuum
  7. Magnitudes and Their Measures
  8. Curves and Surfaces
Appendix; Notes; Bibliography; Index
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