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4 papers · 2 filters
Leibniz's Laws of Continuity and Homogeneity
Mikhail G. Katz, David Sherry
We explore Leibniz's understanding of the differential calculus, and argue that his methods were more coherent than is generally recognized. The foundations of the historical infin…
A Cauchy-Dirac delta function
Mikhail G. Katz, David Tall
The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and…
Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
Mikhail G. Katz, David Sherry
Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's h…
Ten Misconceptions from the History of Analysis and Their Debunking
Piotr Blaszczyk, Mikhail G. Katz, David Sherry
The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesi…