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...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/d13d18f012f6434e84d91c4e892b4564 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | 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. |
|---|