Timeline for Expected symmetry in the diophantine approximations of an irrational number
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2013 at 4:09 | comment | added | Noam D. Elkies | The lower approximants with $\mu \rightarrow 3$ have denominators that are spaced close enough that there can't be any upper approximants with $\mu$ much larger than $2$ (by the usual argument with $|p/q - p'/q'| \geq 1/qq'$). | |
| Dec 13, 2013 at 23:03 | comment | added | Kevin O'Bryant | Do you have a proof that there are no upper ones? I think defining $x$ through its continued fraction may be more tractable, say $x=[0;10,1,100,1,1000,1,\dots]$. | |
| Nov 1, 2013 at 22:35 | vote | accept | Salvo Tringali | ||
| Nov 1, 2013 at 22:32 | comment | added | Salvo Tringali | Right. And the irrationality measure of your $x$ is $3$ (and not $\infty$ as I had previously commented in a hurry). | |
| Nov 1, 2013 at 21:50 | comment | added | Noam D. Elkies | [I wanted to extend the decimal expansion to 81 digits but that made it too wide.] | |
| Nov 1, 2013 at 21:49 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |