Essays on the Theory of Numbers (Dover Books on Mathematics)

Dedekind, Richard

ISBN 10: 0486210103 / ISBN 13: 9780486210100

Published by Dover Publications, New York, 1963

About this Item

Soft cover. Condition: As New. Cover and text in near pristine condition with no marks, tears or folds.

I. Continuity and Irrational Numbers
II. The Nature and Meaning of Numbers

Authorized Translation by Wooster Woodruff Beman.

Seller Inventory # ABE-1770922323970

Bibliographic Details

• Title: Essays on the Theory of Numbers (Dover Books on Mathematics)
• Publisher: Dover Publications, New York
• Publication Date: 1963
• Language: English
• ISBN 10: 0486210103
• ISBN 13: 9780486210100
• Binding: Soft cover
• Condition: As New
• Dimensions: 0.26W x 5.37H x 7.98D inches 0.26 inches width by 5.37 inches height by 7.98 inches depth
• Weight: 2.315 pounds
• Seller catalogs:
  • Education
  • Translated
  • Mathematics

About this title

Synopsis

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.

About the Author

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