Talk:Plateau (mathematics)

I reverted back from the ∀ notation to plain words. This is a general purpose encyclopedia, not a specialized journal. It is good to keep notation no more complicated than necessary. Oleg Alexandrov 20:34, 7 Feb 2005 (UTC)


 * That doesn't make sense to me. If we are to keep things so that anyone can understand them, what are points or &sube; or &fnof; or &rarr; or all those capital letters ?  What is specialized about &forall; when it is used throughout mathematics ?  If the paragraph is headed with "More formally", why is formal notation bad, especially when the previous paragraph explains a plateau plainly with no notation at all ? 131.230.120.16 20:52, 7 Feb 2005 (UTC)


 * I am a PhD in math, so I undertand your point, and love notation myself. And of course you are not required to dumb down math for the general public. But again, why prefer &forall; to "forall"?


 * See How to write a Wikipedia article on Mathematics for some more points about style. The key idea is that our audience is the general public and not other mathematicians.


 * And it would be nice if you indeed make an account. Next time you might be using a different IP address, then you will lose track of the pages you modified. Oleg Alexandrov 21:16, 7 Feb 2005 (UTC)

Definition
I imported the article from planetmath "as is", without thinking much. Now it comes to my mind whether this is a "good" definition. Namely, shouldn't the "plateau" be full-dimensional? I.e., contour lines are not plateaus.

At least the 1-dimensional case hints at this: a single point is clearly not a "plateau". So, what is the actual usage for multivariate functions? Mikkalai 22:00, 7 Feb 2005 (UTC)


 * I don't know these matters, so I cannot answer your question. But most likely this article is right. As you know, mathematicians abuse naming conventions a lot. For example, field (mathematics) has nothing to do with a real field (think flowers and harvest); and ring (mathematics) has something to do with a real ring only in a very particular case. So don't worry if your physical intuition does not seem to correspond to what this definition implies. Oleg Alexandrov 23:09, 7 Feb 2005 (UTC)
 * I am not worried about the intuition; I am worried about the redundancy. The usage of the "plateau" term is pretty widespread for univariate functions, but in this case there is no ambiguity. Like you, I have no idea about the usage in higher dimensions, but to me it is quite natural to separate the  contour lines and the places where the notion of "contour line" fails, which would be "true" plateau. Mikkalai 00:50, 8 Feb 2005 (UTC)

Also, IMO it will make sense to add a comment that (full-dimensional) "plateaus" exist mostly (or only?) in experimental curves (plots) or in piecewise/patched functions/surfaces. I suspect that a "decent" function (e.g., algebraic function) cannot have a full-dimensional plateau. Is that so? If it is, this can explain why this notion is "underdeveloped": no any area of research for a "true" mathematician. Mikkalai 00:50, 8 Feb 2005 (UTC)


 * Honestly, I don't know. If you want, you could go back to planetmath, and ask the author about it. Until then, I would suggest that we leave the article the way it is, because we don't know if what we change is correct or not. What do you think? Oleg Alexandrov 01:39, 8 Feb 2005 (UTC)
 * From the comments of this guy over there it seems that he doesnt know better. By the way, Mathworld doesn't have this term. Mikkalai 01:55, 8 Feb 2005 (UTC)


 * PS Are you Russian? I am Moldavian with a Russian name and poor Russian language skills. Oleg Alexandrov 01:39, 8 Feb 2005 (UTC)
 * No. Belarusian. Mikkalai 01:55, 8 Feb 2005 (UTC)