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Pure mathematics and physical reality (continuity and computability)

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Abstract

Drawing upon the intuitive distinction between real and imaginary mathematical objects (i.e., those that have an actual or potential physical interpretation and those that do not), we propose a mathematical definition of these concepts. Our definition of the class of real objects is based on a certain universal continuous function. We also discuss the class of computable reals, functions, functionals, operators, etc., and we argue that it is too narrow to encompass the class of real objects.

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado, USA

    Jan Mycielski

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  1. Jan Mycielski
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 151–168, 2005.

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Mycielski, J. Pure mathematics and physical reality (continuity and computability). J Math Sci 146, 5552–5563 (2007). https://doi.org/10.1007/s10958-007-0368-y

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  • DOI: https://doi.org/10.1007/s10958-007-0368-y

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