Timeline for What is the simplest, most elementary proof that a particular number is transcendental?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2010 at 2:25 | answer | added | David Feldman | timeline score: 2 | |
| Dec 14, 2010 at 12:03 | answer | added | Pietro Majer | timeline score: 6 | |
| Dec 14, 2010 at 6:43 | answer | added | David Feldman | timeline score: 31 | |
| Dec 14, 2010 at 6:40 | answer | added | Daniel Briggs | timeline score: 46 | |
| Dec 14, 2010 at 5:53 | answer | added | Daniel Litt | timeline score: 5 | |
| Dec 14, 2010 at 5:15 | answer | added | Emerton | timeline score: 14 | |
| Dec 14, 2010 at 4:55 | comment | added | Aaron Meyerowitz | A mind opener for students (at some level) is that since the algebraic numbers are enumerable we can list them (in principle) and put the kth one in the center of an interval of diameter $1/2^k$. Then we have a collection of intervals covering a set of which the (dense) set of rationals is a "tiny" part. But together these intervals have combined length 1 so "most" real numbers are excluded (hence transcendental). At least this shows that our intuition is far from the full story. | |
| Dec 14, 2010 at 4:50 | comment | added | Aaron Meyerowitz | You can describe a fairly short program for a specific enumeration of integer polynomials and use fairly rapid numerical methods to find the real roots to a finite precision. So you can get a number out to a fair number of digits without great grief. But the ease does not matter because there is no real interest in doing it, only that one can (and there are many nice candidates for an order). | |
| Dec 14, 2010 at 4:15 | history | asked | Justin Lanier | CC BY-SA 2.5 |