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Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow
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Tiziana Bascelli ,
Emanuele Bottazzi ,
Frederik Herzberg ,
Vladimir Kanovei ,
Karin Katz ,
Mikhail Katz ,
Tahl Nowik ,
David Sherry ,
Steven Shnider
01 July 2014
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Abstract
Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.