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arXiv · 2106.00229

Infinitesimals via Cauchy sequences: Refining the classical equivalence

Emanuele Bottazzi·Mikhail G. Katz
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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.

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Emanuele Bottazzi, Mikhail G. Katz. 2021-06-01. Infinitesimals via Cauchy sequences: Refining the classical equivalence. https://doi.org/10.1515/math-2021-0048

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