Timeline for Minimum Preserving Transformations [closed]
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 3, 2018 at 20:12 | history | closed |
Wlodek Kuperberg Ben McKay arsmath Pace Nielsen Ilya Bogdanov |
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| Sep 7, 2018 at 21:04 | comment | added | Robert Israel | Actually I think you want it totally ordered. In a partially ordered set, there are two possible meanings of argmin (you may require $f(x)$ to be a minimal element of $f(X)$ or a least element of $f(X)$), and neither of those is preserved by (strictly) monotone increasing functions $g$. The problem is that you could have $g(f(a)) < g(f(b))$ where $f(a)$ and $f(b)$ are incomparable. | |
| Sep 7, 2018 at 16:16 | history | edited | ABIM | CC BY-SA 4.0 |
added 75 characters in body
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| Sep 7, 2018 at 15:39 | comment | added | Pushpendre | Monotonicity is not sufficient, If $g$ is monotone decreasing then the minima is not preserved. Consider $X = [0, 1], f(x) = x, g(x) = 1-x$ | |
| Sep 7, 2018 at 15:32 | comment | added | Robert Israel | I think you mean $f: X \to Y$ and $g: Y \to Z$, where $Y$ and $Z$ are partially ordered sets: otherwise $\text{argmin}$ has no meaning. | |
| Sep 7, 2018 at 15:05 | review | Close votes | |||
| Oct 3, 2018 at 20:12 | |||||
| Sep 7, 2018 at 13:29 | history | asked | ABIM | CC BY-SA 4.0 |