FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 5, PAGES 151-168

Pure mathematics and physical reality (continuity and computability)

J. Mycielski

Abstract

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Drawing upon the intuitive distinction between the real and imaginary mathematical objects (i.e., these which have an actual or potential physical interpretations and these which 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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Last modified: February 26, 2006