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arXiv Open Access 2017

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Tiziana Bascelli Piotr Blaszczyk Alexandre Borovik Vladimir Kanovei Karin U. Katz +5 lainnya
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Abstrak

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. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.

Topik & Kata Kunci

math.HO math.CA math.LO

Penulis (10)

T

Tiziana Bascelli

P

Piotr Blaszczyk

A

Alexandre Borovik

V

Vladimir Kanovei

K

Karin U. Katz

M

Mikhail G. Katz

S

Semen S. Kutateladze

T

Thomas McGaffey

D

David M. Schaps

D

David Sherry

Format Sitasi

APA MLA BibTeX
Bascelli, T., Blaszczyk, P., Borovik, A., Kanovei, V., Katz, K.U., Katz, M.G. et al. (2017). Cauchy's infinitesimals, his sum theorem, and foundational paradigms. https://arxiv.org/abs/1704.07723

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Informasi Jurnal
Tahun Terbit
2017
Bahasa
en
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arXiv
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Open Access ✓