arXiv Open Access 2021

Infinitesimals via Cauchy sequences: Refining the classical equivalence

Emanuele Bottazzi Mikhail G. Katz

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Abstrak

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.

Topik & Kata Kunci

math.LO math.HO

Penulis (2)

Emanuele Bottazzi

Mikhail G. Katz

Format Sitasi

APA MLA BibTeX

Bottazzi, E., Katz, M.G. (2021). Infinitesimals via Cauchy sequences: Refining the classical equivalence. https://arxiv.org/abs/2106.00229

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓