Was sind und was sollen die Zahlen?

This influential 1888 publication explained the real numbers, and their construction and properties, from first principles.

Richard Dedekind (Author)

9781108050388, Cambridge University Press

Paperback / softback, published 2 August 2012

84 pages
21.6 x 14 x 0.5 cm, 0.12 kg

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.

Vorwort
1. Systeme von Elementen
2. Abbildung eines Systems
3. Aehnlichkeit einer Abbildung
4. Abbildung eines Systems in sich selbst
5. Das Endliche und Unendliche
6. Einfach unendliche Systeme
7. Grössere und kleinere Zahlen
8. Endliche und unendliche Theile der Zahlenreihe
9. Definition einer Abbildung der Zahlenreihe durch Induction
10. Die Classe der einfach unendlichen Systeme
11. Addition der Zahlen
12. Multiplication der Zahlen
13. Potenzirung der Zahlen
14. Anzahl der Elemente eines endlichen Systems.

Subject Areas: History of mathematics [PBX]