Timeline for Can infinity shorten proofs a lot?
Current License: CC BY-SA 2.5
7 events
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| Nov 17, 2009 at 22:52 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
Changed an example.
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| Nov 17, 2009 at 22:51 | comment | added | Qiaochu Yuan | Never mind; you can prove the statement by induction, so that was a bad example. | |
| Nov 17, 2009 at 22:41 | comment | added | Qiaochu Yuan | I guess what I meant to say is I don't know of a finitary proof, but now that I think about it, that might not be true. Hmm. | |
| Nov 17, 2009 at 21:22 | comment | added | gowers | You can get the inequality quite easily I think. The log of n! is the sum of log m from 1 to n, which is at least the integral from 1 to n of log x, which is nlogn-n. Done. | |
| Nov 17, 2009 at 20:53 | comment | added | Konrad Swanepoel | You can get $n! \geq n^n/e^n$ just by looking at the Taylor series of $e^x$, but that is perhaps still not hands on. | |
| Nov 17, 2009 at 0:14 | comment | added | Harrison Brown | The elementary proof is far tougher to slog through, although there's a bunch of background hidden in the complex-analytic proof which makes it probably about as hard to learn "from scratch." | |
| Nov 16, 2009 at 23:51 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |