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.
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