On factorial reciprocals in Cantor sets
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908953491800064 |
|---|---|
| author | Lin, Kehao Wu, Yufeng Yang, Siyu |
| author_facet | Lin, Kehao Wu, Yufeng Yang, Siyu |
| contents | Let $C$ be the middle-third Cantor set. We show that \[\left\{\frac{1}{n!}: n\in\mathbb{N}\right\}\cap C=\left\{1, \frac{1}{5!}\right\}.\] This answers a question recently posed by Jiang [J. Lond. Math. Soc., 2026, published online]. Our approach generalizes to general missing-digit sets, showing that, in any such set, there are only finitely many elements of the form $\frac{1}{n!}$, all of which can be effectively determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On factorial reciprocals in Cantor sets Lin, Kehao Wu, Yufeng Yang, Siyu Number Theory 28A80 Let $C$ be the middle-third Cantor set. We show that \[\left\{\frac{1}{n!}: n\in\mathbb{N}\right\}\cap C=\left\{1, \frac{1}{5!}\right\}.\] This answers a question recently posed by Jiang [J. Lond. Math. Soc., 2026, published online]. Our approach generalizes to general missing-digit sets, showing that, in any such set, there are only finitely many elements of the form $\frac{1}{n!}$, all of which can be effectively determined. |
| title | On factorial reciprocals in Cantor sets |
| topic | Number Theory 28A80 |
| url | https://arxiv.org/abs/2603.24614 |