Talk:Concave set

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Clearly, there's something wrong with the following property of a concave set:

(1) A set is called concave if its complement is convex.

A simple counterexample would be a half-space. Let's focus on two-dimensional case, to fix our intuitions. Let h be any half-plane. It is obvious that its complement, -h say, is convex. According to (1) h would be concave, but h is a halfplane and hence convex. A contradiction.


 * There is nothing that says a set couldn't be both convex and concave. I do not see the contradiction. (See also Convex function and Concave function, the same thing holds there too. --13:39, 1 September 2011 (UTC) — Preceding unsigned comment added by 129.16.182.121 (talk)


 * Yeah, a linear function for example is both convex and concave, there's no contradiction here. However a concave set still doesn't really exist, I'm not sure why this page exists. 68.81.4.41 (talk) 01:53, 21 February 2013 (UTC)

I have not read the reference given in the article. Perhaps they define things a tad differently there, so that it all clicks.

The notion of concave set is not correct. Everything that is not a convex set is a non-convex set. — Preceding unsigned comment added by NiccolòFontanaTartaglia (talk • contribs) 07:58, 22 April 2011 (UTC)

If there is no such thing as a "Concave set," why is there a page about it?Trivialsegfault (talk) 01:14, 3 May 2011 (UTC)


 * Agreed. The way this is worded is very odd, as well.  It's not possible for a "notion" to be "correct" or "not correct".  I'm rephrasing it for now.  TricksterWolf (talk) 14:59, 13 January 2012 (UTC)

It seems to me that if the page is to claim that some people advocate the use of the term "concave set", that we would need to offer more than one reference. MathWorld seems like a genuine outlier here. And without a more significant body of evidence I would prefer to explicitly note that MathWorld is an outlier. Mcgrant (talk) 16:37, 23 October 2014 (UTC)

I think the right thing to do here would be to include this language on the "convex set" page, and then redirect all references to "concave set" there. Mcgrant (talk) — Preceding undated comment added 14:01, 24 October 2014 (UTC)

Redirect created. Mcgrant (talk) 14:24, 24 October 2014 (UTC)