On eventually greedy best underapproximations by Egyptian fractions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915030402859008 |
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| author | Kovač, Vjekoslav |
| author_facet | Kovač, Vjekoslav |
| contents | Erdős and Graham found it conceivable that the best $n$-term Egyptian underapproximation of almost every positive number for sufficiently large $n$ gets constructed in a greedy manner, i.e., from the best $(n-1)$-term Egyptian underapproximation. We show that the opposite is true: the set of real numbers with this property has Lebesgue measure zero. [This note solves Problem 206 on Bloom's website "Erdős problems".] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07218 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On eventually greedy best underapproximations by Egyptian fractions Kovač, Vjekoslav Number Theory Classical Analysis and ODEs Combinatorics Erdős and Graham found it conceivable that the best $n$-term Egyptian underapproximation of almost every positive number for sufficiently large $n$ gets constructed in a greedy manner, i.e., from the best $(n-1)$-term Egyptian underapproximation. We show that the opposite is true: the set of real numbers with this property has Lebesgue measure zero. [This note solves Problem 206 on Bloom's website "Erdős problems".] |
| title | On eventually greedy best underapproximations by Egyptian fractions |
| topic | Number Theory Classical Analysis and ODEs Combinatorics |
| url | https://arxiv.org/abs/2406.07218 |