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Somehow, over the years, the article has gone from clear succinct and accurate, to muddy,meandering and misleading. You be best off simply reverting it to a much earlier version...and reflect upon how this happened in the process. 72.228.2.48 ( talk) 17:11, 17 July 2020 (UTC)
I've removed the {{ expand}} template (and Oleg's comment that he had moved it from the main page). I think this article is, if anything, already too long for its subject matter; there's just not that much to say. -- Trovatore 14:15, 6 January 2006 (UTC)
I would suggest adding a softer section at the beginning, or at least a disclaimer that this article assumes a fair comfort with set theory. I suspect many calculus and precalculus students (or their parents) that might want to look at an articles on domain and range would have a bit of trouble with this. I would try to write one but it looks like the consensus is not to expand the article. If it is worth it I would be glad to write something. Thenub314 13:13, 30 September 2006 (UTC)
I find the opening far too difficult. 67.71.156.34 22:16, 5 October 2006 (UTC)
I conjecture that part of the confusion is from the fact that the article starts out with saying the codomain is the set of 'possible' output values and the range is the set of 'actual' output values. This is confusing to say the least, here 'possible' means all values that might be produced including those that cannot be produced for any input! This is only clear once the reader makes it all the way to 'actual outputs' in the next sentence. This would rather non-standard English usage of 'possible'. Wolfram Mathworld treats this topic point without creating confusion; see http://mathworld.wolfram.com/Codomain.html . An example or a link to one might help; there is a simple example at codomain. Perhaps some of the intro should be re-ordered? Many people probably make it through most of life, or at least secondary schooling, equipped with a fuzzy notion of range. Do we need to correct this just to explain the idea of domain? 24.226.31.7 05:47, 19 October 2006 (UTC)
I also found this article confusing. How is something "possible" if it's not "actual"? Thanks for the Wolfram link, but I must say I'm still a little confused. According to that definition, "A set within which the values of a function lie", the codomain of a function could be any number of sets provided that each set contains at least all of the function's actual/possible values. Is that correct? 4.252.2.193 03:35, 14 April 2007 (UTC)
I've read this article as well, before comming to the talk and seeing your message, and I agree, it is very confusing for students. I've put the template up. -- penubag 08:42, 22 January 2008 (UTC)
I found some useful information here, maybe we could use some of it. -- penubag 04:23, 24 January 2008 (UTC)
I've tried to implement some simplifications. Is the page, esp. intro, any better now? Zaslav ( talk) 19:03, 15 March 2010 (UTC)
I'm not going to add this just yet because I'm having a hard time expressing the idea here with clarity. I think we need to mention the terms "domain of definition" and "restricted domain" Here is an attempt:
Usually "domain" means "domain of definition", that is, the set of values for which the function is defined. However, in some contexts, such as complex analysis "domain" refers to a restricted domain. The restricted domain is a subset of the domain of definition. It can be chosen arbitrarily. Some texts use the phrase "domain of definition" for added clarity.
Thoughts? futurebird 01:21, 1 December 2007 (UTC)
I've commented out the image and caption that appear at the top of the page. It stated that the domain of f(x) = √x "is" [0,+∞), but this is only strictly true if we restrict the range of f(x) to not include complex numbers. I think this is very unhelpful, given that the subject of the article concerns such matters. 86.129.77.213 ( talk) 17:39, 3 February 2009 (UTC)
The result of the move request was moved to Domain of a function, which seems to have raised no real objections. Aervanath ( talk) 15:56, 14 June 2009 (UTC)
Domain (mathematics) → Domain (function) — make the title to the point: "(mathematics)" is ambiguous, since there are several mathematical meanings. -- Smjg ( talk) 13:42, 5 June 2009 (UTC)
Originally requested as a {{ db-move}}. Contested by Backslash Forwardslash ( talk · contribs) "not non-controversial: (mathematics) allows for a broader subject base" [1]
Contrary to BF's comment, the other mathematical meanings of "domain" have their own pages, as indicated by both the beginning of Domain (mathematics) and the Domain disambiguation page. Because this page is about just one of these meanings, namely that which is to do with functions, it should be at Domain (function). The whole point of bracketed parts of article titles is to indicate which article is which, which the current title doesn't. -- Smjg ( talk) 13:42, 5 June 2009 (UTC)
The article starts with saying that for a function f : X → Y, X is the domain, and Y is the codomain. It then proceeds by saying that for a well-defined function every element of its domain must be carried to an element of its codomain. In other words, consistent with the practice of most mathematicians, the domain is the set of objects x for which f(x) is defined.
However, in the section of partial functions, it then states that:
"Most mathematicians, including recursion theorists, use the term "domain of f" for the set of all values x such that f(x) is defined. But some, particularly category theorists, consider the domain of a partial function f : X → Y to be X, irrespective of whether f(x) exists for every x in X."
Wait, doesn't this amount to the very same thing then? That is, how are the category theorists saying anything different when they say that the domain of f : X → Y is X given that the article says the very same thing at the very beginning?!?
So: if you want to stick to the practice of most mathematicians, I recommend starting the article either by: "the domain of a function f is the set of all objects x for which a function value f(x) is defined", or you say that "the domain of a function f : X → Y is the set of all elements x in X for which a function value f(x) is defined". Using the latter, you can then continue by saying: "for a well-defined (or total) function f : X → Y, the domain equals X, and for a partial function f : X → Y, the domain is a strict subset of X".
Similarly, instead of saying that the co-domain of a function f : X → Y is Y, you could define the codomain as the set of all elements y in Y for which there is some x in X for which f(x) = y, followed by saying that for a surjective (onto) function, the co-domain equals Y, but that for a non-surjective function, the co-domain is a strict subset of Y.
Wouldn't that be more consistent? — Preceding unsigned comment added by Bram28 ( talk • contribs) 17:11, 28 November 2011 (UTC)
Could somebody expand the text
Any function can be restricted to a subset of its domain. The restriction of to , where , is written .
— Wikipedia contributors, Domain of a function – Wikipedia, the free encyclopedia
by merging in at least some of the content from Function (mathematics) section on Restrictions and Extensions and Restriction (mathematics)?
BCG999 ( talk) 21:14, 3 December 2012 (UTC)
Why are you guys only referring to functions here? Domains to my knowledge exist for mathematical terms (i. e. non-functions) as well! For instance, for , the term is only defined for . Hence, its domain would be written like . The German Wikipedia article (see: de:Definitionsmenge) does have an extra section for the domain of a term; in WP:EN, this is obviously missing (or deemed irrelevant). -andy 77.190.37.140 ( talk) 19:06, 16 March 2013 (UTC)
Can someone explain why the name of this page is Domain of a function, and not Domain (Mathmetics)? FeyBart ( talk) 18:51, 23 June 2013 (UTC)
This
level-5 vital article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
Somehow, over the years, the article has gone from clear succinct and accurate, to muddy,meandering and misleading. You be best off simply reverting it to a much earlier version...and reflect upon how this happened in the process. 72.228.2.48 ( talk) 17:11, 17 July 2020 (UTC)
I've removed the {{ expand}} template (and Oleg's comment that he had moved it from the main page). I think this article is, if anything, already too long for its subject matter; there's just not that much to say. -- Trovatore 14:15, 6 January 2006 (UTC)
I would suggest adding a softer section at the beginning, or at least a disclaimer that this article assumes a fair comfort with set theory. I suspect many calculus and precalculus students (or their parents) that might want to look at an articles on domain and range would have a bit of trouble with this. I would try to write one but it looks like the consensus is not to expand the article. If it is worth it I would be glad to write something. Thenub314 13:13, 30 September 2006 (UTC)
I find the opening far too difficult. 67.71.156.34 22:16, 5 October 2006 (UTC)
I conjecture that part of the confusion is from the fact that the article starts out with saying the codomain is the set of 'possible' output values and the range is the set of 'actual' output values. This is confusing to say the least, here 'possible' means all values that might be produced including those that cannot be produced for any input! This is only clear once the reader makes it all the way to 'actual outputs' in the next sentence. This would rather non-standard English usage of 'possible'. Wolfram Mathworld treats this topic point without creating confusion; see http://mathworld.wolfram.com/Codomain.html . An example or a link to one might help; there is a simple example at codomain. Perhaps some of the intro should be re-ordered? Many people probably make it through most of life, or at least secondary schooling, equipped with a fuzzy notion of range. Do we need to correct this just to explain the idea of domain? 24.226.31.7 05:47, 19 October 2006 (UTC)
I also found this article confusing. How is something "possible" if it's not "actual"? Thanks for the Wolfram link, but I must say I'm still a little confused. According to that definition, "A set within which the values of a function lie", the codomain of a function could be any number of sets provided that each set contains at least all of the function's actual/possible values. Is that correct? 4.252.2.193 03:35, 14 April 2007 (UTC)
I've read this article as well, before comming to the talk and seeing your message, and I agree, it is very confusing for students. I've put the template up. -- penubag 08:42, 22 January 2008 (UTC)
I found some useful information here, maybe we could use some of it. -- penubag 04:23, 24 January 2008 (UTC)
I've tried to implement some simplifications. Is the page, esp. intro, any better now? Zaslav ( talk) 19:03, 15 March 2010 (UTC)
I'm not going to add this just yet because I'm having a hard time expressing the idea here with clarity. I think we need to mention the terms "domain of definition" and "restricted domain" Here is an attempt:
Usually "domain" means "domain of definition", that is, the set of values for which the function is defined. However, in some contexts, such as complex analysis "domain" refers to a restricted domain. The restricted domain is a subset of the domain of definition. It can be chosen arbitrarily. Some texts use the phrase "domain of definition" for added clarity.
Thoughts? futurebird 01:21, 1 December 2007 (UTC)
I've commented out the image and caption that appear at the top of the page. It stated that the domain of f(x) = √x "is" [0,+∞), but this is only strictly true if we restrict the range of f(x) to not include complex numbers. I think this is very unhelpful, given that the subject of the article concerns such matters. 86.129.77.213 ( talk) 17:39, 3 February 2009 (UTC)
The result of the move request was moved to Domain of a function, which seems to have raised no real objections. Aervanath ( talk) 15:56, 14 June 2009 (UTC)
Domain (mathematics) → Domain (function) — make the title to the point: "(mathematics)" is ambiguous, since there are several mathematical meanings. -- Smjg ( talk) 13:42, 5 June 2009 (UTC)
Originally requested as a {{ db-move}}. Contested by Backslash Forwardslash ( talk · contribs) "not non-controversial: (mathematics) allows for a broader subject base" [1]
Contrary to BF's comment, the other mathematical meanings of "domain" have their own pages, as indicated by both the beginning of Domain (mathematics) and the Domain disambiguation page. Because this page is about just one of these meanings, namely that which is to do with functions, it should be at Domain (function). The whole point of bracketed parts of article titles is to indicate which article is which, which the current title doesn't. -- Smjg ( talk) 13:42, 5 June 2009 (UTC)
The article starts with saying that for a function f : X → Y, X is the domain, and Y is the codomain. It then proceeds by saying that for a well-defined function every element of its domain must be carried to an element of its codomain. In other words, consistent with the practice of most mathematicians, the domain is the set of objects x for which f(x) is defined.
However, in the section of partial functions, it then states that:
"Most mathematicians, including recursion theorists, use the term "domain of f" for the set of all values x such that f(x) is defined. But some, particularly category theorists, consider the domain of a partial function f : X → Y to be X, irrespective of whether f(x) exists for every x in X."
Wait, doesn't this amount to the very same thing then? That is, how are the category theorists saying anything different when they say that the domain of f : X → Y is X given that the article says the very same thing at the very beginning?!?
So: if you want to stick to the practice of most mathematicians, I recommend starting the article either by: "the domain of a function f is the set of all objects x for which a function value f(x) is defined", or you say that "the domain of a function f : X → Y is the set of all elements x in X for which a function value f(x) is defined". Using the latter, you can then continue by saying: "for a well-defined (or total) function f : X → Y, the domain equals X, and for a partial function f : X → Y, the domain is a strict subset of X".
Similarly, instead of saying that the co-domain of a function f : X → Y is Y, you could define the codomain as the set of all elements y in Y for which there is some x in X for which f(x) = y, followed by saying that for a surjective (onto) function, the co-domain equals Y, but that for a non-surjective function, the co-domain is a strict subset of Y.
Wouldn't that be more consistent? — Preceding unsigned comment added by Bram28 ( talk • contribs) 17:11, 28 November 2011 (UTC)
Could somebody expand the text
Any function can be restricted to a subset of its domain. The restriction of to , where , is written .
— Wikipedia contributors, Domain of a function – Wikipedia, the free encyclopedia
by merging in at least some of the content from Function (mathematics) section on Restrictions and Extensions and Restriction (mathematics)?
BCG999 ( talk) 21:14, 3 December 2012 (UTC)
Why are you guys only referring to functions here? Domains to my knowledge exist for mathematical terms (i. e. non-functions) as well! For instance, for , the term is only defined for . Hence, its domain would be written like . The German Wikipedia article (see: de:Definitionsmenge) does have an extra section for the domain of a term; in WP:EN, this is obviously missing (or deemed irrelevant). -andy 77.190.37.140 ( talk) 19:06, 16 March 2013 (UTC)
Can someone explain why the name of this page is Domain of a function, and not Domain (Mathmetics)? FeyBart ( talk) 18:51, 23 June 2013 (UTC)