Talk:Support (mathematics)

message: While this is clearly a special point, it is more precise to say that the transform qua distribution has singular support {0} [...]
Qua? --Abdull 04:41, 13 June 2006 (UTC)
thread_title:  qua! qua! 

message: I've taken some analysis, but can't follow this article. It opens
: In mathematics, the support of a real-valued function f on a set X is sometimes defined as the subset of X on which f is nonzero. The most common situation occurs when X is a topological space (such as the real line) and f is a continuous function.
Staying with real-valued functions (e.g., f:R→R) it isn't clear to me if X is a set of real numbers, of real-valued functions, or what. That is, is this saying that the support, S, is defined as
:S = \{ x \in X | f(x) \neq 0 \}
or is it something else? —Ben FrantzDale 13:40, 5 July 2006 (UTC)
thread_title:  Explanation? 

message: In mathematics, the support of a function is, in general, the set of points where the function is not zero. More specifically, a support of a function f from a set X to the real numbers R is a subset Y of X such that f(x) is zero for all x in X that are not in Y.
The "in general" definition is narrower than the "[m]ore specifically" definition! (According to the latter, a function has several supports; according to the former, it has exactly one, which is the smallest possible one according to the latter definition.)
Isn't that backwards? --Army1987!!  09:11, 10 July 2008 (UTC)
replies: text: I've deleted the second sentence.  Clearly someone was confused. Michael Hardy (talk) 21:01, 18 August 2008 (UTC)
replies: text:  The article is still inconsistent in the definition: In "Formulation", it is said that a superset of a support is again a support, contradicting the Introduction's definition.--Roentgenium111 (talk) 22:48, 21 April 2009 (UTC)
thread_title:  Definitions? 

message: How about some examples, instead of talking in generalities all the time?
--212.139.126.204 (talk) 14:54, 18 July 2009 (UTC)
thread_title:  Examples? 

message: I am not sure whether I understood something wrong or if I found a (widespread) mistake. Let us assume: 
* We have a smooth function that is nonzero in the interval (-x, x) and zero in (-inf, -x) and (x, inf). As it is smooth, its value at -x or x has to be equal to its limit in this point, which is 0 by definition. Therefore, this function is obviously nonzero only at the open interval (-x, x). 
* A compact subset of real numbers has to be bounded.  
* Therefore, any such function can never have compact support, as there would have to be a discontinuity at -x, x.
* (This can be probably extended to any smooth function.) 
Can any experienced mathematician correct either me or the article, please? --FDominec (talk) 19:43, 26 October 2009 (UTC)
replies: text: This doesn't seem right. First of all, support has nothing to do with continuity. It is simply the "closure" of a set where a function is nonzero. In other words, a function that is only nonzero on (-x, x) has a compact support, since it is nonzero on the open interval and therefore its support, the closure of the interval, is compact. -- Taku (talk) 22:46, 26 October 2009 (UTC)
replies: text: I see, there is In mathematics, the support of a function is the set of points where the function is not zero, or the closure of that set. in the support article. As far as I can remember, we considered the support not to be a closure of anything at the school, just the set of nonzero points. Nevertheless, it should be rewritten more clearly. --FDominec (talk) 14:34, 27 October 2009 (UTC)
replies: text: Yes it could be better worder. Is this one definition (it's one or the other depending on context), or two competing definitions (some authors define it one way, other the other)? I'm guessing the latter, given what you say and that Wolfram Mathworld only gives the closure version. In that case, which definition has been chosen for this Wikipedia article? Dependent Variable (talk) 13:38, 2 March 2011 (UTC)
thread_title:  Compact support 

message: "In mathematics, the support of a function is the set of points where the function is not zero-valued, or the closure of that set.[1]:678".
In "[1]:678" it states:
:"The support of a continuous function u is the closure of the set {x | u(x) =/= 0} and is denoted by the symbol supp(u)."
Thus the given source doesn't source wp's definition, as "function" and "continuous function" is something different. So either wp's definition has to be changed or another source has to be given. Futhermore "set [...] not zero-valued, or the closure of that set" partly implies that one can choice (maybe based on different definitions) which set it is or that the author/wp doesn't know which set it is. Accourding to the mentioned source it's always the closure of that set (though the closure of that set might be the same as that set).-Yodonothav (talk) 10:37, 26 November 2012 (UTC)
thread_title:  Definition/source 

message: I think this sentence, from the Compact Support section, is problematic:
Functions with compact support in X are those with support that is a compact subset of X. For example, if X is the real line, they are functions of bounded support and therefore vanish at infinity (and negative infinity).
While technically it is true that such functions vanish at infinity, it is a weak statement—they vanish considerably sooner than infinity.
I initially thought that "and therefore [the functions] vanish at infinity" was intended as justification for why functions of bounded support also have compact support. I realized my mistake as soon as I clicked "vanish at infinity" and read the definition. There is no further mention of vanishing at infinity, so I think that it is distracting to bring it up at all. Does anyone else feel the same way? I don't usually edit Wikipedia (except to correct grammar or spelling), so I'm not sure what to do about this.  — Preceding unsigned comment added by 137.22.232.216 (talk) 21:58, 17 January 2013 (UTC)
thread_title:  Vanishing at infinity 

message: I have changed "and" to "or" in the definition. The definition doesn't seem to make sense with an "and" in it. 
There can be several meanings of "support", but (within one chosen meaning) "the support" has to be either ... or ...
Bj norge (talk) 09:39, 2 July 2013 (UTC)
thread_title:  Definition 

message: There seems to be a contradiction between the definition at the top (support "is the set of points where the function is not zero-valued, or the closure of that set" - taking into account the definition of closure) and the later statement that "any superset of a support is also a support". If the term is used with many different meanings then this should be made clear from the beginning in such a way that the article is self-consistent.  — Preceding unsigned comment added by 192.76.7.215 (talk) 14:39, 26 September 2013 (UTC)
replies: text: I made some edits to address some of the points above, but I agree that there's still some confusion between a support for a function and the support. Maybe this is due, in part, to the term "support" being used in different ways in different areas? Reader634 (talk) 21:09, 12 January 2014 (UTC)

text: I reworked the section on "Formulation" since (lacking references) I don't believe it's usual to define supports so that "any superset of a support is also a support". Reader634 (talk) 07:47, 14 January 2014 (UTC)
thread_title:  Confusion 

message: My immediate reaction to the current intro paragraph is to ask the next classic big ‘W’: why? Why is it all but those that map to zero? What is the purpose?? A good overview intro should answer the questions what, why, where and possibly who and do all those things in simple terms.  — Preceding unsigned comment added by 2600:387:6:805:0:0:0:B1 (talk) 15:03, 13 August 2019 (UTC)
thread_title:  question/suggestion