What makes a theory of infinitesimals useful? A view by Klein and Fraenkel

2018/02/01 by Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz +1 · 1 citation
Mathematics · #math.HO #math.CA #math.LO #msc:26E35 #msc:03A05

paper · pdf · doi:10.5642/jhummath.201801.07

published as Journal of Humanistic Mathematics, Volume 8 Issue 1 (January 2018), pages 108-119 · 10 pages, published in Journal of Humanistic Mathematics http://scholarship.claremont.edu/jhm/vol8/iss1/7/

arxiv created 2018/02/01 · arxiv updated 2018/02/07

Abstract

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

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• A Philosophical History of Infinitesimals

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