Timeline for Function with range equal to whole reals on every open set
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2014 at 3:32 | comment | added | Nate Eldredge | @QuinnCulver: No, I don't think so. By my reading the number $.++1$ is in that interval and maps to 1. | |
| Dec 26, 2011 at 15:53 | comment | added | Quinn Culver | Isn't Conway's function constantly zero on the interval $[.++,.+++]$ (using Wikipedia's notation)? So strictly speaking, the function's range isn't $\mathbb{R}$ on every open set | |
| Dec 11, 2010 at 18:32 | comment | added | gowers | Actually, I take that back -- I still hadn't completely understood Conway's example. | |
| Dec 11, 2010 at 18:26 | comment | added | gowers | But that applies equally to the examples based on limiting density. | |
| Dec 11, 2010 at 17:01 | comment | added | Aaron Meyerowitz | @gowers The ease with which one can specify an explicit pre-image of any real in any target domain interval. | |
| Dec 11, 2010 at 14:50 | comment | added | gowers | These comments make me feel a bit slow: what does Conway's function have over the simpler functions given in several of the answers below? | |
| Jul 17, 2010 at 6:42 | vote | accept | falagar | ||
| Jul 17, 2010 at 5:23 | comment | added | Pedro Teixeira | OK, I don't have anything to add here, other than to say that this was the coolest thing I learned today. Wow! | |
| Jul 16, 2010 at 16:50 | comment | added | Vectornaut | Why does everything Conway does end up making me cry? ^_^ p.s. I think that function definitely belongs here: mathoverflow.net/questions/22189/… | |
| Jul 16, 2010 at 11:06 | comment | added | Willie Wong | Wow, that is a fabulous example. | |
| Jul 16, 2010 at 7:13 | history | answered | Robin Chapman | CC BY-SA 2.5 |