TL;DR
The paper discusses the ring of fluxions, a rigorous mathematical structure for infinitesimals that offers an alternative to Robinson's approach, but has been largely overlooked despite its elementary nature.
Contribution
It introduces and analyzes the ring of fluxions, providing a rigorous foundation for infinitesimals distinct from existing methods.
Findings
The ring of fluxions captures intuitive properties of infinitesimals.
It offers an elementary and rigorous alternative to Robinson's approach.
The existence of this ring has been historically ignored.
Abstract
The ring of fluxions (real sequential germs at infinity) provides a rigorous approach to infinitesimals, different from the better-known approach of Abraham Robinson. The basic idea was first espoused in a paper by Curt Schmieden and Detlof Laugwitz published in 1958. Although this ring codifies all the usual intuitive properties of infinitesimals in a very elementary way, its existence has been generally ignored.
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Taxonomy
TopicsMathematical and Theoretical Analysis · History and Theory of Mathematics · Advanced Topology and Set Theory