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25 Remote Warehouse Mathematics- General

Essays on the Theory of Numbers

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Essays on the Theory of Numbers Cover

 

Synopses & Reviews

Publisher Comments:

This volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.

The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.

The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

Synopsis:

Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.

Synopsis:

Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the 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

Product Details

ISBN:
9780486210100
Translator:
Beman, Wooster W.
Author:
Beman, Wooster W.
Author:
Mathematics
Author:
Dedekind, Richard
Publisher:
Dover Publications
Subject:
Mathematics
Subject:
Number Theory
Subject:
Algebra - General
Subject:
Modern mathematics
Subject:
General Mathematics
Subject:
Mathematics - Algebra
Subject:
Mathematics - General
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19630631
Binding:
TRADE PAPER
Language:
English
Pages:
128
Dimensions:
8.5 x 5.38 in 0.32 pd

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Related Subjects


Metaphysics » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory

Essays on the Theory of Numbers New Trade Paper
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Product details 128 pages Dover Publications - English 9780486210100 Reviews:
"Synopsis" by ,
Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.
"Synopsis" by , Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.
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