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.
| Original language | English |
|---|---|
| Pages (from-to) | 477-482 |
| Number of pages | 6 |
| Journal | Open Mathematics |
| Volume | 19 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2021 |
Bibliographical note
Publisher Copyright:© 2021 Emanuele Bottazzi and Mikhail G. Katz, published by De Gruyter 2021.
Funding
This work was supported by a grant of the Government of Russian Federation through Resolution No. 220, Agreement No. 11.G34.31.0042.
| Funders | Funder number |
|---|---|
| Government Council on Grants, Russian Federation | 220 |
Keywords
- Cauchy sequence
- hyperreal
- infinitesimal
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