Open Mathematics (Jun 2021)

Infinitesimals via Cauchy sequences: Refining the classical equivalence

  • Bottazzi Emanuele,
  • Katz Mikhail G.

DOI
https://doi.org/10.1515/math-2021-0048
Journal volume & issue
Vol. 19, no. 1
pp. 477 – 482

Abstract

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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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