Who gave you the Cauchy-Weierstrass tale? The dual history of rigorous calculus

DOI10.1007/s10699-011-9235-xzbMath1279.01017arXiv1108.2885OpenAlexW2072656382WikidataQ55877841 ScholiaQ55877841MaRDI QIDQ351452

Mikhail G. Katz, Alexandre V. Borovik

Publication date: 11 July 2013

Published in: Foundations of Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2885

zbMATH Keywords

convergencecontinuitylimitscontinuumultraproductsum theoreminfinitesimalBernoulliCauchyWeierstrassDirac functiontransfer principle\(\varepsilon\)-\(\delta\) techniquesArchimedean axiomdu Bois-ReymondepsilonticsFelix Kleinfoundations of analysishyperrealsStolz

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) History of mathematics in the 19th century (01A55) History of real functions (26-03)

Related Items (22)

Is Leibnizian calculus embeddable in first order logic? ⋮ Toward a history of mathematics focused on procedures ⋮ Gregory's sixth operation ⋮ Cauchy's infinitesimals, his sum theorem, and foundational paradigms ⋮ Euler's lute and Edwards's oud ⋮ Small oscillations of the pendulum, Euler's method, and adequality ⋮ Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics ⋮ The Mathematical Intelligencer flunks the Olympics ⋮ A Cauchy-Dirac delta function ⋮ Ten misconceptions from the history of analysis and their debunking ⋮ Periodic words connected with the tribonacci-Lucas numbers ⋮ Cauchy's work on integral geometry, centers of curvature, and other applications of infinitesimals ⋮ 19th-century real analysis, forward and backward ⋮ Large-\( N\) limits of spaces and structures ⋮ Leibniz's infinitesimals: their fictionality, their modern implementations, and their foes from Berkeley to Russell and beyond ⋮ The notion of variable quantities \(\omega\) in Bolzano's early works ⋮ Did Weierstrass’s differential calculus have a limit-avoiding character? His definition of a limit inϵ–δstyle ⋮ An integer construction of infinitesimals: toward a theory of eudoxus hyperreals ⋮ Toward a clarity of the extreme value theorem ⋮ Almost Equal: the Method of Adequality from Diophantus to Fermat and Beyond ⋮ Proofs and retributions, or: why Sarah can't take limits ⋮ Controversies in the foundations of analysis: comments on Schubring's \textit{Conflicts}

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