Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms

Tiziana Bascelli, Piotr Błaszczyk, Alexandre Borovik, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, David M. Schaps, David Sherry

    Research output: Contribution to journalArticlepeer-review


    Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms.Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

    Original languageEnglish
    Pages (from-to)1-30
    Number of pages30
    JournalFoundations of Science
    Early online date24 Jun 2017
    Publication statusPublished - 2017


    • Cauchy’s infinitesimal
    • Foundational paradigms
    • Quantifier alternation
    • Sum theorem
    • Uniform convergence


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