Infinitesimals via Cauchy sequences: Refining the classical equivalence
Logic
2021-06-02 v1 History and Overview
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.
Cite
@article{arxiv.2106.00229,
title = {Infinitesimals via Cauchy sequences: Refining the classical equivalence},
author = {Emanuele Bottazzi and Mikhail G. Katz},
journal= {arXiv preprint arXiv:2106.00229},
year = {2021}
}
Comments
8 pages, to appear in Open Mathematics