Infinitesimals via Cauchy sequences: Refining the classical equivalence

Emanuele Bottazzi; Mikhail G. Katz

doi:10.1515/math-2021-0048

Infinitesimals via Cauchy sequences: Refining the classical equivalence

Emanuele Bottazzi, Mikhail G. Katz

Department of Mathematics

University of Pavia

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	477-482
Number of pages	6
Journal	Open Mathematics
Volume	19
Issue number	1
DOIs	https://doi.org/10.1515/math-2021-0048
State	Published - 1 Jan 2021

Bibliographical note

Publisher Copyright:
© 2021 Emanuele Bottazzi and Mikhail G. Katz, published by De Gruyter 2021.

Funding

This work was supported by a grant of the Government of Russian Federation through Resolution No. 220, Agreement No. 11.G34.31.0042.

Funders	Funder number
Government Council on Grants, Russian Federation	220

Keywords

Cauchy sequence
hyperreal
infinitesimal

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10.1515/math-2021-0048

Cite this

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Infinitesimals via Cauchy sequences: Refining the classical equivalence

Abstract

Bibliographical note

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Keywords

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