Infinitesimals via Cauchy sequences: Refining the classical equivalence
arXiv:2106.00229 · doi:10.1515/math-2021-0048
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.
arXiv comment8 pages, to appear in Open Mathematics
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