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9780486210100

Essays on the Theory of Numbers

by
  • ISBN13:

    9780486210100

  • ISBN10:

    0486210103

  • Format: Paperback
  • Copyright: 1963-06-01
  • Publisher: Dover Publications

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Summary

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

Continuity and Irrational Numbers
Preface
Properties of Rational Numbers
Comparison of the Rational Numbers with the Points of a Straight Line
Continuity of the Straight Line
Creation of Irrational Numbers
Continuity of the Domain of Real Numbers
Operations with Real Numbers
Infinitesimal Analysis
The Nature and Meaning of Numbers
Prefaces
Systems of Elements
Transformation of a System
Similarity of a Transformation
Similar Systems
Transformation of a System in Itself
The Finite and Infinite
Simply Infinite Systems
Series of Natural Numbers
Greater and Less Numbers
Finite and Infinite Parts of the Number-Series
Definition of a Transformation of the Number-Series by Induction
The Class of Simply Infinite Systems
Addition of Numbers
Multiplication of Numbers
Involution of Numbers
Number of the Elements of a Finite System
Table of Contents provided by Publisher. All Rights Reserved.

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