Cambridge University Press eBooks· 2012
Was sind und was sollen die Zahlen?
- 176citations
- 2012year
Short summary
Richard Dedekind's 1888 book resolved foundational issues in calculus by constructing real numbers from rational numbers using the 'Dedekind cut' method.
AI-generated from the title and abstract; the full text is not read.
Key points
- 19th-century mathematics replaced calculus paradoxes with rigorous analysis.
- Real numbers were identified as the fundamental basis for all analysis.
- Dedekind constructed real numbers from rational numbers using the 'Dedekind cut'.
- Dedekind's method is still central to mathematics and was generalized for surreal numbers.
AI-generated from the title and abstract; the full text is not read.
Abstract
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 authors' abstract, as published at the source. Cambridge University Press eBooks, 2012 · DOI ↗
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Field: Theoretical Computer Science
Theoretical Computer ScienceMathematics