Article ID: CBB001252715

Ten Misconceptions from the History of Analysis and Their Debunking (2013)

unapi

The widespread idea that infinitesimals were eliminated by the great triumvirate of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.

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Authors & Contributors
Katz, Mikhail G.
Ferreirós, José
Mechthild Koreuber
Haffner, Emmylou
Schubring, Gert
Schlimm, Dirk
Concepts
Mathematics
Mathematical analysis
Infinitesimals
Set theory
Calculus
Philosophy
Time Periods
19th century
20th century, early
20th century, late
18th century
17th century
Places
Germany
France
Italy
Europe
China
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