# Book:Richard Dedekind/Essays on the Theory of Numbers

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## Richard Dedekind: *Essays on the Theory of Numbers*

Published $1901$, **The Open Court Publishing Company**.

### Online copies

### Contents

- I. CONTINUITY AND THE IRRATIONAL NUMBERS
- Preface
- I. Properties of Rational Numbers
- II. Comparison of the Rational Numbers with the Points of a Straight Line
- III. Continuity of the Straight Line
- IV. Creation of the Irrational Numbers
- V. Continuity of the Domain of Real Numbers
- VI. Operations with Real Numbers
- VII. Infinitesimal Analysis

- II. THE NATURE AND MEANING OF NUMBERS
- Prefaces
- I. Systems of Elements
- II. Transformation of a System
- III. Similarity of a Transformation. Similar Systems
- IV. Transformation of a System in Itself
- V. The Finite and Infinite
- VI. Simply Infinite Systems. Series of Natural Numbers
- VII. Greater and Less Numbers
- VIII. Finite and Infinite Parts of a Number-Series
- IX. Definition of a Tranformation of the Number-Series by Induction
- X. The Class of Simply Infinite Systems
- XI. Addition of Numbers
- XII. Multiplication of Numbers
- XIII. Involution of Numbers
- XIV. Number of the Elements of a Finite System