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.

中文翻译：

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通过柯西序列的无穷小：改进经典等价

柯西序列之间经典等价关系的改进产生了一个有用的无穷小富集数系统。这种方法可以被看作是将 Cauchy 的观点形式化，即零序列“变成”无穷小。我们在 Giuseppe Peano 1910 年的出版物中指出了一个鲜为人知的无穷小系统构造，扭转了他早先对康托尔贬低无穷小的认可。