Infinitesimals via Cauchy sequences: Refining the classical equivalence

Open Mathematics

Bottazzi Emanuele¹  Katz Mikhail G.² 

[1] Department of Mathematics F. Casorati, University of Pavia, Via Ferrata, 5, 27100, Pavia, Italy;Department of Mathematics, Bar Ilan University, Ramat Gan, 5290002, Israel;

关键词: cauchy sequence;    hyperreal;    infinitesimal;    03h05;    26e35;   

DOI  :  10.1515/math-2021-0048

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown