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Journal Nonlinear World №9 for 2013 г.
Article in number:
Some aspects of formation of numerical systems raising efficiency of special transformation of data
Keywords: infinity actual infinity fractal numerical system image of a point scaling fractal paradigm
Authors:
A.V. Strukov - Ph.D. (Eng.), Corresponding Fellow of Academy of Engineering Sciences of Name A.M. Prokhorov, Scientific Secretary of the Section «Information security» of the Russian Scientific and Technical Society of Radio Engineering, Electronics and Communication of Name A.S. Popov. E-mail: strukovi14@yandex.ru
Abstract:
Development of algorithm of creation of a new numerical row on the basis of natural accident - a task difficult and interesting. For the solution of this task authors used some theories. First theory. The classical theory of great number of the Cantor, being the basic theory in conducted researches. Second theory. The alternative theory of great number of P. Vopenk is modern interpretation of the classical theory of the sets, allowing to answer the majority of the questions closed before the researcher in the classical theory. Third theory. Paradoxes of infinite B. Bolzano. This theory is the additional theory to the basic theory. It shows a look of the Czech mathematician of the XVIII century Bernard Boltsano on the paradoxes arising at modeling of infinite space. The theory is very useful when carrying out the analysis and comparison of options of definition of concept of a point and concept of infinity for the purpose of development to them uniform concepts. Fourth theory. Continuity and R. Dedekind's irrational numbers. Mathematical calculations from this theory also found the realization as the additional theory to the classical theory. Fifth theory. Concepts of a fractal paradigm and the global fractal method, for the first time A.A. Potapov-s entered in works which should be applied to questions stated in this work.
Pages: 672-678
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