Abstract
A number operator has been introduced based upon the binary (p-nary) presentation of numbers. This operator acts upon a numerical state vector. Generally the numerical state vector describes numbers that are not precise but smeared in a quantum sense. These states are interpreted in wave logic terms, according to which concepts may exist within the inner language of a phenomenon that in principle cannot be translated into the language of the investigator. In particular, states may exist where mean values of a quantity, continuous in classical limits, take only discrete values. Operators for differentiation and integration of operator functions are defined, which take the usual form in the classical limit.
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References
Orlov, Yu. F. (1974). On a possible effect of the manner of arranging physical quantities upon the state of a physical system (unpublished).
Orlov, Yu. F. (1975). Group theory approach to logic. The wave logic. I, II. International Congress of Logic, Methodology and Philosophy of Science. Canada, 1975, pp. 37–38.
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Orlov, Y.F. Wave calculus based upon wave logic. Int J Theor Phys 17, 585–598 (1978). https://doi.org/10.1007/BF00673010
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DOI: https://doi.org/10.1007/BF00673010