Timeline for answer to A question on subgroup-restricted irrationality measures by Anthony Quas
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26, 2014 at 7:17 | comment | added | Steven Stadnicki | For the most part; the one concern I see is in the spacing, since there's no guarantee of uniformity across the range. Still, it looks like the core concept - there are only polynomially many numbers in an exponentially-sized range, so you can't expect any sort of density of the sort needed here - is a solid one. | |
| Apr 26, 2014 at 6:59 | comment | added | Anthony Quas | @Steven Stadnicki: Is my argument convincing to you? It seemed to be ignored by the OP. | |
| Apr 26, 2014 at 1:45 | comment | added | Steven Stadnicki | (Wait, silly mistake on my part - the dyadics aren't a subgroup under multiplication, only addition, as e.g. the inverse of $\frac32$ isn't in this group. The group of powers of 2, of course, isn't dense in $\mathbb{Q}^+$.) | |
| Apr 25, 2014 at 21:28 | comment | added | Steven Stadnicki | This doesn't make sense to me - it seems like the measure has to be at least $1$, since for every $q$ there's some $p$ with $\left|\frac pq-x\right|\lt\frac1q$. Certainly this holds for e.g. the dyadics. | |
| Nov 25, 2013 at 19:08 | history | answered | Anthony Quas | CC BY-SA 3.0 |