Interpreting Euler in anĪrchimedean conceptual framework obscures important aspects of Euler's work. Of quantity is symptomatic of a post-Weierstrassian placement of Euler in theĪrchimedean track for the development of analysis, as well as a blurring of theĭistinction between the dual tracks noted by Bos. Second, analysis of the scope of the Law of Continuity famously formulated by Leibniz and mapping it onto this (RPI) structure. ![]() We argue that Ferraro's assumption that Euler worked with a classical notion The Leibnizian law of continuity similarly Euler's principle of cancellation is compared to the Leibnizian American Heritage Science Similar definitions Synonyms: minute microscopic imperceptible unnoticeable small insignificant tiny minuscule little Antonyms: substantial significant large huge big noun An infinitesimal quantity. Terms of a Weierstrassian notion of limit and Fraser declares classicalĪnalysis to be a "primary point of reference for understanding theĮighteenth-century theories." Meanwhile, scholars like Bos and Laugwitz seek toĮxplore Eulerian methodology, practice, and procedures in a way more faithfulĮuler's use of infinite integers and the associated infinite products isĪnalyzed in the context of his infinite product decomposition for the sineįunction. Websters New World Capable of having values approaching zero as a limit. Infinitesimal mathematics, as when Ferraro proposes to understand Euler in Weierstrass's ghost behind some of the received historiography on Euler's Mathematical practice (or the structures mathematicians use in practice) toĮxamine contrasting interpretations of infinitesimal mathematics of the 17thĪnd 18th century, in the work of Bos, Ferraro, Laugwitz, and others. ![]() Download a PDF of the paper titled Interpreting the infinitesimal mathematics of Leibniz and Euler, by Jacques Bair and 12 other authors Download PDF Abstract: We apply Benacerraf's distinction between mathematical ontology and
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