Any superset of a support is also a support

[Rasalhague]

"any superset of a support is also a support"

Wikipedia:

In mathematics, the support of a function is the set of points where the function is not zero, or the closure of that set. [...] any superset of a support is also a support

Let f:R-->R: f(x) = 1 if x is in (-1,1), otherwise let f(x) = 0. Then support₁ of f, "the set of points where the function is not zero" is (-1,1), and support₂ of f, "the closure of that set", is [-1,1]. In either case, there is a proper superset of the support, i.e. a superset of the support which is not equal to either kind of support, for example (-2,2).

Is the article mistaken, or have I misunderstood it? Does it perhaps mean "any superset of a support of one function is also a support of a function, not necessarily the same function", that is, "for every superset, S, of a support of one function, f, there is a function g such that S is a support of g"?

 

[Stephen Tashi]

Which Wikipedia article contains that statement? Is there any criticism of it on the discussion page for the article?

 

[Office_Shredder]

In the article, you quote from the general description at the top, and then skip to what's written in the definition below. If you read the whole "Formulation" paragraph, specifically the first line, it says a function is supported on Y if it is zero on Y's complement, and Y is called A support. THE support of a function is often used to refer to the smallest possible support of the function

 

[Rasalhague]

Sorry, I meant to link to it:

http://en.wikipedia.org/wiki/Support_(mathematics)

Yes, there is an objection to that statement, in a section called "Definition?"

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)

There hasn't been any response to it. But looking at this again, I think I see that apparently an earlier version of the article began:

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.

And thanks to Office_Shredder's hint, I see that the Formulation section of the article, does actually begin with a version of this definition, support₃: "A function supported in Y must vanish in X \ Y", according to which a support needn't be unique. And the section ends with mention of further possible, context dependent meanings. The following section, Closed supports, suggests why support₃ may not have been mentioned in the intro; it says support₂ is the definition used in "the most common situation" (when X is a topological space [...] and f : X→R is a continuous function."

I should have read further.

 

[Office_Shredder]

The terminology is not 100% consistent, but that's pretty much true in how it's used in the rest of math. It's usually easiest to just use context to decide which form of support somebody is using