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Article ID: CBB001252715

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

Błaszczyk, Piotr (Author)
Katz, Mikhail G. (Author)
Sherry, David M. (Author)

Foundations of Science
Volume: 18, no. 1
Issue: 1
Pages: 43-74

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Mathematics Mathematical analysis Infinitesimals 19th century 20th century, early Germany Dedekind, Richard Weierstrass, Karl Theodor Cantor, Georg Ferdinand Ludwig

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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