Timeline for Associative mean
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 20, 2017 at 14:28 | comment | added | Yaakov Baruch | See my comment to the OP for a very nice concrete example. | |
| Nov 19, 2017 at 16:51 | comment | added | Yaakov Baruch | Even more: no continuous mean at all can arise from this construct. | |
| Nov 19, 2017 at 16:07 | comment | added | Yaakov Baruch | NIce! A visualization of $m$ in the upper-left half plane $a\le b$: let $L_1$ the least $\sqsubset$-element of $\mathbb{R}$, $L_2$ the 2nd least etc. Then $R_1=m^{-1}(L_1)$ is the largest possible rectangle rooted in $(L_1,L_1)$, i.e. a rectangle with $(L_1,L_1)$ as lower-right corner, possibly extending to infinity in the up and/or left direction. $R_2=m^{-1}(L_2)$ will then be the largest possible rectangle rooted on $(L_2,L_2)$ not overlapping with $R_1$. And so on for $R_3$ etc. This picture also shows that not all monotonic means can arise from your construct. | |
| Nov 15, 2017 at 21:01 | history | edited | Goldstern | CC BY-SA 3.0 |
monotone - yes, continuous - no.
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| Nov 14, 2017 at 0:40 | history | edited | Goldstern | CC BY-SA 3.0 |
better proof of m(a,m(b,c))=d
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| Nov 14, 2017 at 0:21 | history | answered | Goldstern | CC BY-SA 3.0 |