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ISBN13: 978-0486210100

ISBN10: 0486210103 Edition: 63

Copyright: 1963

Publisher: Dover Publications, Inc.

Published: 1963

International: No

ISBN10: 0486210103 Edition: 63

Copyright: 1963

Publisher: Dover Publications, Inc.

Published: 1963

International: No

Two most important essays by the famous German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, thereby a rigorous meaning of continuity in analysis. The other is an attempt to give logical basis for transfinite numbers and properties of the natural numbers.

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

ISBN10: 0486210103 Edition: 63

Copyright: 1963

Publisher: Dover Publications, Inc.

Published: 1963

International: No

Two most important essays by the famous German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, thereby a rigorous meaning of continuity in analysis. The other is an attempt to give logical basis for transfinite numbers and properties of the natural numbers.

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

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