Infinitesimals via Cauchy sequences: Refining the classical equivalence

Emanuele Bottazzi; Mikhail G. Katz

doi:https://doi.org/10.1515/math-2021-0048

Infinitesimals via Cauchy sequences: Refining the classical equivalence

Emanuele Bottazzi, Mikhail G. Katz

Department of Mathematics

Bar-Ilan University

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

Keywords

Cauchy sequence
hyperreal
infinitesimal

All Science Journal Classification (ASJC) codes

General Mathematics

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Cite this

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Infinitesimals via Cauchy sequences: Refining the classical equivalence

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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