@article{b5dea339ec804b6a9dcdb1b154561f8a,
title = "Cauchy{\textquoteright}s Infinitesimals, His Sum Theorem, and Foundational Paradigms",
abstract = "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{\textquoteright}s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms.Cauchy{\textquoteright}s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy{\textquoteright}s proof closely and show that it finds closer proxies in a different modern framework.",
keywords = "Cauchy{\textquoteright}s infinitesimal, Foundational paradigms, Quantifier alternation, Sum theorem, Uniform convergence, DEFINITION, Cauchy's infinitesimal, DIFFERENTIALS, EPSILON",
author = "Tiziana Bascelli and Piotr B{\l}aszczyk and Alexandre Borovik and Vladimir Kanovei and Katz, {Karin U.} and Katz, {Mikhail G.} and Kutateladze, {Semen S.} and Thomas McGaffey and Schaps, {David M.} and David Sherry",
year = "2018",
month = jun,
day = "1",
doi = "10.1007/s10699-017-9534-y",
language = "English",
volume = "23",
pages = "267--296",
journal = "Foundations of Science",
issn = "1233-1821",
publisher = "Springer Netherlands",
number = "2",
}