Infinitesimals via Cauchy sequences: Refining the classical equivalence
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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.
1989 ◽
Vol 41
(5)
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pp. 830-854
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2020 ◽
Vol 112
(6)
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pp. 1167-1182
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2015 ◽
Vol E98.A
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pp. 1310-1312
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2017 ◽
Vol 8
(3)
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pp. 189-200
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