Timeline for What is a strict definition of U-shaped relationship?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| S Nov 29, 2017 at 16:07 | history | bounty ended | Neznajka | ||
| S Nov 29, 2017 at 16:07 | history | notice removed | Neznajka | ||
| Nov 29, 2017 at 16:07 | vote | accept | Neznajka | ||
| Nov 25, 2017 at 10:00 | answer | added | scottkosty | timeline score: 8 | |
| Nov 24, 2017 at 15:05 | comment | added | amoeba | I don't think "U-shaped" is a mathematically well-defined term; there is no universally accepted definition and I don't think you should be looking for one. I changed the first two sentences of my answer to stress that. | |
| Nov 24, 2017 at 14:40 | comment | added | whuber♦ | I couldn't attest to a general agreement--and I'm sure that many authors would object that my definition is broader than they intended. That's why I have left it as a comment. | |
| Nov 24, 2017 at 14:39 | comment | added | Neznajka | @whuber This is exactly what I am looking for -- if there is a general agreement on how to define it.... | |
| Nov 24, 2017 at 13:40 | comment | added | whuber♦ | Different authors may have different definitions--should the relation be continuous? Differentiable? Convex? The most general definition consistent with the idea of "increasing then decreasing" or "decreasing then increasing" is: A map $f:A\to\mathbb{R}$ with $A\subset\mathbb{R}$ is "U-shaped" means there exists a decomposition of $A=B\cup C$ where (1) every element of $B$ is less than or equal to every element of $C$; (2) $f$ is monotonic on both $B$ and $C$; (3) the images $f(B)$ and $f(C)$ have at least two values each; and (4) the directions of monotonicity of $f$ differ on $B$ and $C$. | |
| Nov 24, 2017 at 13:34 | history | tweeted | twitter.com/StackStats/status/934052685292232704 | ||
| Nov 24, 2017 at 11:33 | answer | added | amoeba | timeline score: 7 | |
| Nov 24, 2017 at 11:20 | history | edited | amoeba |
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| S Nov 24, 2017 at 10:55 | history | bounty started | Neznajka | ||
| S Nov 24, 2017 at 10:55 | history | notice added | Neznajka | Authoritative reference needed | |
| Nov 22, 2017 at 9:44 | history | edited | Neznajka | CC BY-SA 3.0 |
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| Nov 22, 2017 at 9:38 | history | asked | Neznajka | CC BY-SA 3.0 |