On the interchangeability of sequences leading to an infinite decimal decomposition

Authors: Askerova A.A.
Published in issue: #8(25)/2018
DOI: 10.18698/2541-8009-2018-8-356
Category: Mathematics | Chapter: Computational Mathematics
Keywords: formula, decimal decomposition, sequence of numbers, principles of the theory of limits, theory of real numbers, space, infinity, test of convergence
Published: 08.08.2018

The article presents a complete justification for the fact that a sequence of numbers characterizing an irrational number can be replaced by an equivalent sequence leading to infinite decomposition. Based on the previously developed theory of real numbers, it is justified that to each real number can be associated with a fundamental sequence that will be its decimal decomposition, and vice versa. The conditions that a given decimal decomposition must meet are also given. In addition, the question of the influence of the rationality and irrationality of a number on the form of its decimal decomposition is considered, namely, that rational numbers have a periodic decomposition. The converse is also true.

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