The ring of Fermat reals

DOI10.1016/j.aim.2010.04.010zbMath1205.26051OpenAlexW2066916943MaRDI QIDQ1959453

Paolo Giordano

Publication date: 7 October 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2010.04.010

zbMATH Keywords

smooth infinitesimal analysisnilpotent infinitesimalsextension of the real fieldactual infinitesimals

Mathematics Subject Classification ID

Nonstandard models in mathematics (03H05) Miscellaneous topics in real functions (26E99) Nonstandard analysis (26E35)

Related Items (10)

Smooth infinitesimals in the metaphysical foundation of spacetime theories ⋮ Who gave you the Cauchy-Weierstrass tale? The dual history of rigorous calculus ⋮ Ten misconceptions from the history of analysis and their debunking ⋮ New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem ⋮ Nests, and Their Role in the Orderability Problem ⋮ 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 ⋮ Homomorphisms between rings with infinitesimals and infinitesimal comparisons

Cites Work

• The rise of non-Archimedean mathematics and the roots of a misconception. I: The emergence of non-Archimedean systems of magnitudes
• Full algebra of generalized functions and non-standard asymptotic analysis
• A ring homomorphism is enough to get nonstandard analysis
• Classical mechanics as quantum mechanics with infinitesimal \(\hslash\)
• A purely algebraic characterization of the hyperreal numbers
• Differential geometry, Lie groups and symmetric spaces over general base fields and rings
• Function Theory on Some Nonarchimedean Fields
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