Was sind und was sollen die Zahlen?
Author:   Richard Dedekind
Publisher:   Springer Fachmedien Wiesbaden
Edition:   9. Aufl. 1961
ISBN:  

9783663008750


Pages:   47
Publication Date:   01 January 1961
Format:   Paperback
Availability:   In Print   Availability explained
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Was sind und was sollen die Zahlen?


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Overview

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.

Full Product Details

Author:   Richard Dedekind
Publisher:   Springer Fachmedien Wiesbaden
Imprint:   Vieweg+Teubner Verlag
Edition:   9. Aufl. 1961
Dimensions:   Width: 14.80cm , Height: 0.30cm , Length: 21.00cm
Weight:   0.103kg
ISBN:  

9783663008750


ISBN 10:   3663008754
Pages:   47
Publication Date:   01 January 1961
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.
Language:   German

Table of Contents

1. Systeme von Elementen.- 2. Abbildung eines Systems.- 3. AEhnlichkeit einer Abbildung. AEhnliche Systeme.- 4. Abbildung eines Systems in sich selbst.- 5. Das Endliche und Unendliche.- 6. Einfach unendliche Systeme. Reihe der naturlichen Zahlen.- 7. Groessere und kleinere Zahlen.- 8. Endliche und unendliche Teile der Zahlenreihe.- 9. Definition einer Abbildung der Zahlenreihe durch Induktion.- 10. Die Klasse der einfach unendlichen Systeme.- 11. Addition der Zahlen.- 12. Multiplikation der Zahlen.- 13. Potenzierung der Zahlen.- 14. Anzahl der Elemente eines Systems.

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