Infinitesimals via Cauchy sequences: Refining the classical equivalence
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 infin...
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| Main Authors: | , |
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| Format: | article |
| Language: | EN |
| Published: |
De Gruyter
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/d13d18f012f6434e84d91c4e892b4564 |
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| Summary: | 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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