Talk:Domain (mathematics)

From Wikipedia, the free encyclopedia

WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: Start Class Mid Priority  Field: Basics

Contents

[edit] Removed expansion template

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)

Good! :) Oleg Alexandrov (talk) 22:15, 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)

If you can make the lead section more accessible (while keeping it accurate!) by all means do. That's not the sort of expansion we (if I may presume to speak for Oleg) are concerned about. "Expansion" suggests finding more to say, not saying it more understandably; I fear the only way to find more material about this topic is to let it devolve into trivia. --Trovatore 20:35, 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)

[edit] Confusing

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)

That's right. Any set containing all the values is a valid codomain. You see, saying that "function's codomain is the real numbers" is the same as saying "function takes real values". Practically speaking it is much easier to say where a function takes values than what all the values are. Oleg Alexandrov (talk) 05:10, 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)

Can you explain what you find confusing? If you don't, it's quite hard for anyone to try to remedy the problem. — Carl (CBM · talk) 12:31, 22 January 2008 (UTC)
It's confusing in a number of ways: It does not clearly explain exactly what is the domain. It does not clearly state the domain's relation with respect to the x-axis. When read from a student's POV, the article just sounds like mesh, no clear statements are generally being said, I would fix it, but I understand the difficulty of doing this. -- penubag  19:03, 23 January 2008 (UTC)
The domain of an abstract function will not be related to the x axis in any particular way. That would only apply to functions defined on the real line. The article begins with the sentence "In mathematics, a domain is most often defined as the set of values, D for which a function is defined." - which seems like a clear enough definition. I am also interested in improving the article; but I'm not sure exactly what you are seeing. — Carl (CBM · talk) 19:04, 23 January 2008 (UTC)
I agree with Carl here. The definition as given seems reasonably clear. Something might be added to the article stating that when considering the graphical representation of a function, particularly functions whose domain is some subset of the real numbers, the domain is often represented as a subset of the horizontal axis (often called the x-axis) of a Cartesian plane. Not sure that such an addition would be particularly helpful, though. Perhaps penubag can pick a particular sentence which is found to be confusing, and we can work from there. Paul August ☎ 21:26, 23 January 2008 (UTC
The definition provided is confusing for students. "In mathematics, a domain is most often defined as the set of values, D for which a function is defined." D? what's D? for a which a function is defined? Any function? Maybe a quick definition of function would be great. According to here there are 3 different definitions (but those provided are still rather unclear). The definition in Prentice Hall PreCalculus states that the domain of a function is the function's limit with respect to the x axis, while the range of the function is the graph's limit with respect to the y axis. Surely this should be somewhere stated in our article. Also this seems confusing (or that I find confusing), "A function that has a domain N is said to be a function over N, where N is an arbitrary set." What is N? We should state that it just a variable representing the domain. (is it?) It has a domain N to be a function over N? As in a fraction? A little confusing. Basically saying, only one that is really familiar with math could make since out of what's being said, as a student's POV, it is really hard to grasp this concept, perhaps fixing some terminology could alleviate it. -- penubag  04:20, 24 January 2008 (UTC)

I found some useful information here, maybe we could use some of it. -- penubag  04:23, 24 January 2008 (UTC)

The issue with the Mathworld refs is that they say the same thing as this article: "The term domain is most commonly used to describe the set of values D for which a function (map, transformation, etc.) is defined." "(1) The set of values for which a function is defined." I don't mind giving an example involving a function from the reals to the reals, but the concept of domain is for a general function, and in the end must be handled as such. — Carl (CBM · talk) 04:29, 24 January 2008 (UTC)
Yeah, I know, but we have the opportunity to fix ours to a concise level, I'm just not a math guy, so I wouldn't know how to best do this. -- penubag  04:56, 24 January 2008 (UTC)

[edit] new section?

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:

[edit] Domain of definition

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)