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

## Richard Dedekind: Essays on the Theory of Numbers

Published $1901$, The Open Court Publishing Company.

### 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