Bøger af Richard Dedekind

Dieses Buch bietet eine umfassende Einführung in die Zahlentheorie, die sich sowohl an Anfänger als auch an erfahrene Mathematiker richtet. Die Vorlesungen behandeln die grundlegenden Themen der Zahlentheorie wie zum Beispiel Zahlenbereiche, Kongruenzen und quadratische Formen. Es ist ein Must-Have für jeden, der sich für Mathematik interessiert.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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

""�����ber die Elemente der Theorie der Euler'schen Integrale"" ist ein Buch des deutschen Mathematikers Richard Dedekind, das erstmals im Jahr 1852 ver������ffentlicht wurde. Das Buch besch�����ftigt sich mit der Theorie der Euler'schen Integrale, die eine wichtige Rolle in der Analysis spielen. Dedekind erkl�����rt die grundlegenden Konzepte der Theorie und gibt eine detaillierte Darstellung der Eigenschaften der Euler'schen Integrale. Er beschreibt auch die Beziehung zwischen den Euler'schen Integralen und anderen wichtigen mathematischen Konzepten wie der Gamma-Funktion und der Riemannschen Zeta-Funktion. Das Buch ist ein wichtiger Beitrag zur Mathematik und hat dazu beigetragen, die Theorie der Euler'schen Integrale weiterzuentwickeln.This Book Is In German.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This Is A New Release Of The Original 1901 Edition.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

§ 1. VORSTELLUNG DES ZAHLENGEBIETES Wir konnen jede ganze Zahl bildlich oder geometrisch darstellen. Nehmen wir zum Beispiel eine Linie von beliebiger Lange an, und auf derselben einen Punkt o. So konnen wir die Zahl eins so darstellen, indem wir eine beliebige konstante Lange auf dieser vom Nullpunkt aus nach rechts auftragen. Dieses Stuck reprasen­ tirt uns also die Zahl eins. Wollen wir die Zahl 2 geometrisch darstellen, so wissen wir, dass 2 = 1 + 1 ist. Wir haben also nur die Einheit zweimal vom Nullpunkt aus aufzutragen, oder von 1 aus noch einmal und erhalten das geometrische Bild der Zahl 2 . Urn das Bild der Zahl 3 zu erhalten, konnen wir unsere Langeneinheit dreimal vom Nullpunkt aus auftragen. Ebenso k- nen wir 4,5,6,7,8 ... bis bildlich darstellen. Wollen wir hingegen eine gebrochene Zahl geometrisch darstellen, zum Beispiel t, so waren wir dies mit unsern Langeneinheiten 7 3 3 nicht imstande, denn 4 = 14 ' und 4 ist eine Grosse, die kleiner ist als 1. Wir mussen daher unsere Lange in noch klei­ nere Theile eintheilen und zwar in Viertel. Dann sind wir erst 7 imstande, 4 geometrisch darzustellen.

The nineteenth century saw the paradoxes and obscurities of eighteenth-century calculus gradually replaced by the exact theorems and statements of rigorous analysis. It became clear that all analysis could be deduced from the properties of the real numbers. But what are the real numbers and why do they have the properties we claim they do? In this charming and influential book, Richard Dedekind (1831-1916), Professor at the Technische Hochschule in Braunschweig, showed how to resolve this problem starting from elementary ideas. His method of constructing the reals from the rationals (the Dedekind cut) remains central to this day and was generalised by Conway in his construction of the 'surreal numbers'. This reissue of Dedekind's 1888 classic is of the 'second, unaltered' 1893 edition.

The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir 'Sur la Theorie des Nombres Entiers Algebriques' first appeared in instalments in the 'Bulletin des sciences mathematiques' in 1877. This is a translation of that work by John Stillwell, who also adds a detailed introduction that gives the historical background as well as outlining the mathematical obstructions that Dedekind was striving to overcome. Dedekind's memoir gives a candid account of his development of an elegant theory as well as providing blow-by-blow comments as he wrestled with the many difficulties encountered en route. A must for all number theorists.