Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers
In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs \({g_0<1}\) and \(g_1=g_0-1\). Transformations (bijections of the set to itself) of interval \([0,g_0]\) preserving tails of this representation of numbers are studied. We prove co...
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| Date: | 2020 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2020
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1498 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs \({g_0<1}\) and \(g_1=g_0-1\). Transformations (bijections of the set to itself) of interval \([0,g_0]\) preserving tails of this representation of numbers are studied. We prove constructively that the set of all continuous transformations from this class with respect to composition of functions forms an infinite non-abelian group such that increasing transformations form its proper subgroup. This group is a proper subgroup of the group of transformations preserving frequencies of digits of representations of numbers. |
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