Infinitesimals via Cauchy sequences: Refining the classical equivalence

A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy’s sentiment that a null sequence “becomes” an infinitesimal. We signal a little-noticed construction of a system with infin...

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Main Authors:	Bottazzi Emanuele, Katz Mikhail G.
Format:	article
Language:	EN
Published:	De Gruyter 2021
Subjects:	cauchy sequence hyperreal infinitesimal 03h05 26e35 Mathematics QA1-939
Online Access:	https://doaj.org/article/d13d18f012f6434e84d91c4e892b4564
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spelling	oai:doaj.org-article:d13d18f012f6434e84d91c4e892b45642021-12-05T14:10:53ZInfinitesimals via Cauchy sequences: Refining the classical equivalence2391-545510.1515/math-2021-0048https://doaj.org/article/d13d18f012f6434e84d91c4e892b45642021-06-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0048https://doaj.org/toc/2391-5455A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy’s sentiment that a null sequence “becomes” an infinitesimal. We signal a little-noticed construction of a system with infinitesimals in a 1910 publication by Giuseppe Peano, reversing his earlier endorsement of Cantor’s belittling of infinitesimals.Bottazzi EmanueleKatz Mikhail G.De Gruyterarticlecauchy sequencehyperrealinfinitesimal03h0526e35MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 477-482 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	cauchy sequence hyperreal infinitesimal 03h05 26e35 Mathematics QA1-939
spellingShingle	cauchy sequence hyperreal infinitesimal 03h05 26e35 Mathematics QA1-939 Bottazzi Emanuele Katz Mikhail G. Infinitesimals via Cauchy sequences: Refining the classical equivalence
description	A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy’s sentiment that a null sequence “becomes” an infinitesimal. We signal a little-noticed construction of a system with infinitesimals in a 1910 publication by Giuseppe Peano, reversing his earlier endorsement of Cantor’s belittling of infinitesimals.
format	article
author	Bottazzi Emanuele Katz Mikhail G.
author_facet	Bottazzi Emanuele Katz Mikhail G.
author_sort	Bottazzi Emanuele
title	Infinitesimals via Cauchy sequences: Refining the classical equivalence
title_short	Infinitesimals via Cauchy sequences: Refining the classical equivalence
title_full	Infinitesimals via Cauchy sequences: Refining the classical equivalence
title_fullStr	Infinitesimals via Cauchy sequences: Refining the classical equivalence
title_full_unstemmed	Infinitesimals via Cauchy sequences: Refining the classical equivalence
title_sort	infinitesimals via cauchy sequences: refining the classical equivalence
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/d13d18f012f6434e84d91c4e892b4564
work_keys_str_mv	AT bottazziemanuele infinitesimalsviacauchysequencesrefiningtheclassicalequivalence AT katzmikhailg infinitesimalsviacauchysequencesrefiningtheclassicalequivalence
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Infinitesimals via Cauchy sequences: Refining the classical equivalence

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