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

doi:10.1007/s10699-017-9534-y

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

Кафедра математического анализа ММФ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

5 Цитирования (Scopus)

Аннотация

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.

Язык оригинала	английский
Страницы (с-по)	267-296
Число страниц	30
Журнал	Foundations of Science
Том	23
Номер выпуска	2
DOI	https://doi.org/10.1007/s10699-017-9534-y
Состояние	Опубликовано - 1 июн 2018

Предметные области OECD FOS+WOS

6.05 ПРОЧИЕ ГУМАНИТАРНЫЕ НАУКИ
6.01.MQ ИСТОРИЯ И ФИЛОСОФИЯ НАУКИ

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10.1007/s10699-017-9534-y

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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.",

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Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms. / Bascelli, Tiziana; Błaszczyk, Piotr; Borovik, Alexandre; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Kutateladze, Semen S.; McGaffey, Thomas; Schaps, David M.; Sherry, David.

В: Foundations of Science, Том 23, № 2, 01.06.2018, стр. 267-296.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

TY - JOUR

T1 - Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms

AU - Bascelli, Tiziana

AU - Błaszczyk, Piotr

AU - Borovik, Alexandre

AU - Kanovei, Vladimir

AU - Katz, Karin U.

AU - Katz, Mikhail G.

AU - Kutateladze, Semen S.

AU - McGaffey, Thomas

AU - Schaps, David M.

AU - Sherry, David

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - Cauchy’s infinitesimal

KW - Foundational paradigms

KW - Quantifier alternation

KW - Sum theorem

KW - Uniform convergence

KW - DEFINITION

KW - Cauchy's infinitesimal

KW - DIFFERENTIALS

KW - EPSILON

UR - http://www.scopus.com/inward/record.url?scp=85021226787&partnerID=8YFLogxK

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DO - 10.1007/s10699-017-9534-y

M3 - Article

AN - SCOPUS:85021226787

VL - 23

SP - 267

EP - 296

JO - Foundations of Science

JF - Foundations of Science

SN - 1233-1821

IS - 2

ER -

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

Аннотация

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