Timeline for Famous results about the value of a given limit assuming it exists
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 20, 2016 at 20:59 | vote | accept | Sylvain JULIEN | ||
| Apr 7, 2016 at 13:16 | comment | added | Nate Eldredge | One way to have such a result would be to show that a subsequence converges to a particular limit. Iosif Pinelis's LLN example is of this form. Another similar example would be to show that the sequence converges in a weaker topology. | |
| Apr 7, 2016 at 13:05 | answer | added | Ryan O'Donnell | timeline score: 4 | |
| Apr 7, 2016 at 0:19 | comment | added | Terry Tao | Not quite of this form, but zero-one laws are certainly famous: en.wikipedia.org/wiki/Zero%E2%80%93one_law | |
| Apr 6, 2016 at 23:10 | comment | added | Gerry Myerson | On a much lower level, if the limit of the sequence $$\sqrt2,\sqrt2^{\sqrt2},\sqrt2^{\sqrt2^{\sqrt2}},\dots$$ exists, then it must be a solution of $\sqrt2^x=x$, hence, 2 (or 4). | |
| Apr 6, 2016 at 20:33 | answer | added | Iosif Pinelis | timeline score: 6 | |
| Apr 6, 2016 at 20:17 | comment | added | Steve Huntsman | See section 2 of cs.toronto.edu/~yuvalf/CLT.pdf (also perhaps books.google.com/books?id=Q4XzBwAAQBAJ as mentioned in section 10 of the PDF), from which I quote: "the real content of the central limit theorem is that convergence does take place. The exact form of the basin of attraction is deducible beforehand - the only question is whether summing up lots of independent variables and normalizing them accordingly would get us closer and closer to the only possible limit, a normal distribution with the limiting mean and variance." | |
| Apr 6, 2016 at 19:26 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Fixed a typo.
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| Apr 6, 2016 at 19:23 | history | asked | Sylvain JULIEN | CC BY-SA 3.0 |