Timeline for What numbers can be approximated "pretty well" by rationals?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Oct 25, 2010 at 20:40 | comment | added | Felipe Voloch | @Douglas: Now I am confused, too many double negations. Most numbers can be well approximated. | |
| Oct 25, 2010 at 20:32 | comment | added | Douglas Zare | For intuition, large coefficients in the simple continued fraction expansion produce good rational approximations. There is a limiting distribution for the coefficients, the Gauss-Kuzmin distribution, which is supported on all positive integers, so you expect that with some coarse independence that you get infinitely many coefficients greater than any fixed size except on a set of measure $0$. | |
| Oct 25, 2010 at 20:14 | comment | added | Douglas Zare | If I read it correctly, the answer is yes, almost all real numbers can be approximated pretty well by rationals. | |
| Oct 24, 2010 at 14:58 | vote | accept | Qiaochu Yuan | ||
| Oct 24, 2010 at 14:56 | comment | added | Felipe Voloch | eom.springer.de/d/d032580.htm | |
| Oct 24, 2010 at 14:47 | comment | added | Qiaochu Yuan | Thanks, Felipe! I can't seem to find a statement of Khinchin's theorem (I assume you're not referring to the theorem about Khinchin's constant) online. Do you have a reference? | |
| Oct 24, 2010 at 14:30 | history | answered | Felipe Voloch | CC BY-SA 2.5 |