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Algebra of Real Functions: Classification of Functions, Fictitious and Essential Functions
Pure and Applied Mathematics Journal
Volume 8, Issue 4, August 2019, Pages: 72-76
Received: Jul. 25, 2019; Accepted: Aug. 15, 2019; Published: Sep. 3, 2019
Author
Maydim Malkov, Department of Mathematics, Russian Research Center for Artificial Intelligence, Moscow, Russia
Article Tools Abstract PDF (223KB)
Abstract
Real numbers are divided into fictitious (non-computable) and essential (computable). Fictitious numbers do not have numerical values, essential numbers have algorithms for constructing these numbers with any exactness. The set of fictitious numbers is continual, the set of essential numbers is countable. Functions are also divided into fictitious, defined over the set of fictitious numbers, and essential, defined over the set of essential numbers. Essential functions have an algorithm for calculating any value with any exactness. All functions of applied mathematics and some functions of abstract mathematics are essential The set these functions is countable. The four upper levels of classification of real functions are constructed. This classification uses superpositions of functions and diagonal sets borrowed from the algebra of finite-valued functions.
Keywords
Algebra of Real Functions, Algebra of Superpositions, Computable Real Functions, Computable Real Numbers
Maydim Malkov, Algebra of Real Functions: Classification of Functions, Fictitious and Essential Functions, Pure and Applied Mathematics Journal. Vol. 8, No. 4, 2019, pp. 72-76. doi: 10.11648/j.pamj.20190804.11
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