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Introduction: Advancing Non-Archimedean Mathematics

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Advances in Non-Archimedean Analysis and Applications

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Abstract

Hermann Weyl is quoted with saying in Philosophie der Mathematik und Naturwissenschaft 1927, p. 36: As a matter of fact, it is by no means impossible to build up a consistent “non-Archimedean” theory of magnitudes in which the axiom of Eudoxus (usually named after Archimedes) does not hold. Indeed the Axiom of Eudoxus/Archimedes is the main difference between the real and p-adic/ultrametric space; however the axiom is more of a physical one which concerns the process of measurement: exchanging the real numbers field with the p-adic number field is tantamount to exchanging axiomatics in quantum physics.

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Authors and Affiliations

  1. Department of Mathematics, Howard University, Washington, DC, USA

    Bourama Toni

  2. School of Mathematical and Statistical Sciences, University of Texas, Austin, TX, USA

    W. A. Zúñiga-Galindo

  3. Centro de Investigación y Estudios Avanzados del IPN, Mexico, Mexico

    W. A. Zúñiga-Galindo

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  1. Bourama Toni
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Correspondence to Bourama Toni or W. A. Zúñiga-Galindo .

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Editors and Affiliations

  1. University of Texas Rio Grande Valley, Brownsville, TX, USA

    W. A. Zúñiga-Galindo

  2. Department of Mathematics, Howard University, Washington, DC, USA

    Bourama Toni

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Toni, B., Zúñiga-Galindo, W.A. (2021). Introduction: Advancing Non-Archimedean Mathematics. In: Zúñiga-Galindo, W.A., Toni, B. (eds) Advances in Non-Archimedean Analysis and Applications. STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham. https://doi.org/10.1007/978-3-030-81976-7_1

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