Infinitesimals without logic

DOI10.1134/S1061920810020032zbMath1264.26035arXiv0909.3954OpenAlexW3103287392MaRDI QIDQ455512

J. Herrera, D. Rodríguez-Gómez

Publication date: 22 October 2012

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3954

zbMATH Keywords

Fermat realsnilpotent infinitesimals

Mathematics Subject Classification ID

Nonstandard models in mathematics (03H05) Nonstandard analysis (26E35)

Related Items (9)

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography ⋮ Who gave you the Cauchy-Weierstrass tale? The dual history of rigorous calculus ⋮ A Cauchy-Dirac delta function ⋮ Ten misconceptions from the history of analysis and their debunking ⋮ New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem ⋮ Categorical frameworks for generalized functions ⋮ Calculus in the ring of Fermat reals. I: Integral calculus ⋮ Fermat-Reyes method in the ring of Fermat reals ⋮ Topological and algebraic structures on the ring of Fermat reals

Cites Work

• A ring homomorphism is enough to get nonstandard analysis
• A purely algebraic characterization of the hyperreal numbers
• Differential geometry, Lie groups and symmetric spaces over general base fields and rings
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