Timeline for Real functions with finitely many zeroes
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 25, 2012 at 11:15 | answer | added | Thierry Zell | timeline score: 2 | |
| Oct 16, 2012 at 17:00 | answer | added | Gerhard Paseman | timeline score: 0 | |
| Oct 16, 2012 at 15:01 | vote | accept | Yair Carmon | ||
| Oct 16, 2012 at 13:14 | answer | added | Emil Jeřábek | timeline score: 6 | |
| Oct 16, 2012 at 9:28 | answer | added | Markus Schweighofer | timeline score: 2 | |
| Oct 15, 2012 at 21:35 | comment | added | Rabee Tourky | A very general class (of continuous functions) is continuous piecewise increasing or decreasing functions with finite components. If it has an odd number of affine components and its first piece is increasing, then the last piece is increasing. | |
| Oct 15, 2012 at 21:10 | comment | added | Gerald Edgar | @Yir: true, my class is too general | |
| Oct 15, 2012 at 19:47 | answer | added | Aaron Meyerowitz | timeline score: 0 | |
| Oct 15, 2012 at 19:18 | comment | added | Yair Carmon | But $cos(x)$ is complex-analytic and has infinitely many zeros... | |
| Oct 15, 2012 at 16:49 | comment | added | Gerald Edgar | A general class: complex-analytic (in a neighborhood of $\mathbb R^+$). | |
| Oct 15, 2012 at 15:04 | comment | added | Yair Carmon | Gerald - while I don't see what's not "elementary" in the function you mentioned, I'd love to hear ideas for other classes of functions for which the finite number of zeros property is provable. | |
| Oct 15, 2012 at 14:39 | comment | added | Igor Khavkine | I meant that $\log(x+1)$ is not eventually concave. Though perhaps I'm misunderstanding something about the motivation part of your question... ah, it seems that for you $f$ is some specific function that you didn't define, rather any function. | |
| Oct 15, 2012 at 14:09 | answer | added | André Schlichting | timeline score: 0 | |
| Oct 15, 2012 at 13:50 | comment | added | Lierre | Can you show us the explicit formula you have for $f$ ? Do you have a differential equation ? | |
| Oct 15, 2012 at 13:01 | comment | added | Gerald Edgar | You need something better than the vague definition of "elementary function" in Wikipedia. For example (on $\mathbb R$) is $\sqrt{x^2}-x = |x|-x$ supposed to be called "elementary"? I don't think so, but you can't see that from the Wikipedia definition. | |
| Oct 15, 2012 at 12:45 | history | edited | Yair Carmon | CC BY-SA 3.0 |
edited body
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| Oct 15, 2012 at 11:04 | comment | added | Yair Carmon | Why so? It seems to me $log(1+x)$ equals 0 only once... | |
| Oct 15, 2012 at 10:53 | comment | added | Igor Khavkine | Isn't $\log(x+1)$ a counterexample? | |
| Oct 15, 2012 at 10:35 | history | asked | Yair Carmon | CC BY-SA 3.0 |