A two-symbol system of encoding and some of its applications

• Date: 2025
• Main Authors: Pratsiovytyi, Mykola, Lysenko, Iryna, Ratushniak, Sofiia
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2025
• Subjects: two-symbol system of encoding (representation) of numbers; \(G_2\)-representation of numbers; cylindrical set (cylinder); left and right shift operator; tail set; group of continuous transformations of real interval preserving tails; 11H71; 26A46; 93B17
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2395
• Journal Title: Algebra and Discrete Mathematics

The article is devoted to a two-symbol system of encoding for real numbers with two bases of different signs \(g_0 \in (0;\frac{1}{2}]\) and \(g_1\equiv g_0-1\), as well as its applications in metric number theory and the metric theory of functions. We prove that any natural number \(a\) can be repr...