Infinitesimals via Cauchy sequences: Refining the classical equivalence

@article{Bottazzi2021InfinitesimalsVC,
  title={Infinitesimals via Cauchy sequences: Refining the classical equivalence},
  author={Emanuele Bottazzi and Mikhail G. Katz},
  journal={Open Mathematics},
  year={2021},
  volume={19},
  pages={477 - 482}
}
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. 

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