Essays on the Theory of Numbers (Second Edition)

by Richard Dedekind, Wooster Woodruff Beman (Translator)

Overview

Included in this volume are two essays on the theory of numbers: "Continuity and Irrational Numbers" and "The Nature and Meaning of Numbers." The text is an authorized translation by Wooster Woodruff Beman, Professor of Mathematics in the University of Michigan.

Product Details

ISBN-13:	9781434499912
Publisher:	Brownstone Books
Publication date:	11/08/2024
Pages:	64
Product dimensions:	6.69(w) x 9.61(h) x 0.13(d)

Table of Contents

I. Continuity and Irrational Numbers
    Preface
  1. Properties of Rational Numbers
  2. Comparison of the Rational Numbers with the Points of a Straight Line
  3. Continuity of the Straight Line
  4. Creation of Irrational Numbers
  5. Continuity of the Domain of Real Numbers
  6. Operations with Real Numbers
  7. Infinitesimal Analysis
II. The Nature and Meaning of Numbers
    Prefaces
  1. Systems of Elements
  2. Transformation of a System
  3. Similarity of a Transformation. Similar Systems
  4. Transformation of a System in Itself
  5. The Finite and Infinite
  6. Simply Infinite Systems. Series of Natural Numbers
  7. Greater and Less Numbers
  8. Finite and Infinite Parts of the Number-Series
  9. Definition of a Transformation of the Number-Series by Induction
  10. The Class of Simply Infinite Systems
  11. Addition of Numbers
  12. Multiplication of Numbers
  13. Involution of Numbers
  14. Number of the Elements of a Finite System