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Kronecker. On the concept of number. (Kronecker. Sur le concept de nombre.) (French) Zbl 0935.01007

The author introduces and reproduces an 1887 article on the number concept by Leopold Kronecker (1823-1891), which appeared in a collection of papers in honour of Edouard Zeller, a historian of Greek philosophy. Unlike his contemporaries who founded analysis on a broadening of the number concept, Kronecker rather sought to restrict it to entities immediately derivable from positive whole numbers. His paper treats basic cardinal arithmetic, negative and rational numbers defined using arithmetic modulo linear polynomials and real algebraic numbers as entities contained in intervals formed by analyzing signs of the values of their defining polynomials.

MSC:

01A55 History of mathematics in the 19th century
01A75 Collected or selected works; reprintings or translations of classics
03-03 History of mathematical logic and foundations

Biographic References:

Kronecker, L.
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