Timeline for Can formally differentiating give a derivative of a discrete function?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2011 at 1:30 | vote | accept | Steven Gubkin | ||
| Mar 4, 2011 at 1:57 | answer | added | Matt Young | timeline score: 10 | |
| Mar 4, 2011 at 0:32 | answer | added | Gerry Myerson | timeline score: 14 | |
| Mar 3, 2011 at 23:34 | comment | added | Qiaochu Yuan | Bouncing off of Andrey's comment, you might look for a function f holomorphic in a neighborhood of the real line whose real values on the real line are discrete but such that its derivative has real values on some real interval. By the identity principle, the values of its derivative on that real interval uniquely determine it, and every elementary function I can think of which takes real values on some interval is real everywhere, so... | |
| Mar 3, 2011 at 23:13 | comment | added | Andrey Rekalo | It seems that the main problem with $f(x)$ in your example is that $x$ is implicitly assumed to be real. Formal manipulations with elementary functions (including formal differentiation) can be often easily justified if $x$ is allowed to be complex. | |
| Mar 3, 2011 at 22:46 | history | asked | Steven Gubkin | CC BY-SA 2.5 |