The monoid of numbers of the form 1 < a^q /b^p < a
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913193034514432 |
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| author | Fallot, Laurent |
| author_facet | Fallot, Laurent |
| contents | This paper is a study of the set of rational numbers of the form 1 < a^q /b^p < a with a and b co-prime integers. The set F (a,b) of these numbers, with an appropriate binary law, is a monoid isomorphic to (N, +, 0). We identify the sequences of minimum and maximum record holders in F (a,b) and prove that the first one converges to 1 while the second one converges to a. We conclude that F (a,b) is dense in the set of the real numbers comprise between 1 and a. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06248 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The monoid of numbers of the form 1 < a^q /b^p < a Fallot, Laurent General Topology Number Theory This paper is a study of the set of rational numbers of the form 1 < a^q /b^p < a with a and b co-prime integers. The set F (a,b) of these numbers, with an appropriate binary law, is a monoid isomorphic to (N, +, 0). We identify the sequences of minimum and maximum record holders in F (a,b) and prove that the first one converges to 1 while the second one converges to a. We conclude that F (a,b) is dense in the set of the real numbers comprise between 1 and a. |
| title | The monoid of numbers of the form 1 < a^q /b^p < a |
| topic | General Topology Number Theory |
| url | https://arxiv.org/abs/2312.06248 |