Talk:Domain of a function

message: 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)
thread_title: Article was better in 2006

message: I've removed the  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)
replies: text: Good! :) Oleg Alexandrov (talk) 22:15, 6 January 2006 (UTC)

text: 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)
thread_title: Removed expansion template

message: 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:
===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)
replies: text: "Domain of definition", while not widely used, is correct and is obviously a good term to introduce in the exposition.  I am doing that.  "Restricted domain" is more specialized and I think it's treated well in defining the restriction of a function, in the article. Zaslav (talk) 18:57, 15 March 2010 (UTC)
thread_title: new section?

message: 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)
replies: text: "Domain of definition", while not widely used, is correct and is obviously a good term to introduce in the exposition.  I am doing that.  "Restricted domain" is more specialized and I think it's treated well in defining the restriction of a function, in the article. Zaslav (talk) 18:57, 15 March 2010 (UTC)
thread_title: Domain of definition

message: 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)
thread_title: Problematic image

message: Could somebody expand the text  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)
thread_title:  Definition expansion 

message: 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 x \in \R, the term \sqrt{x-1} is only defined for x >= 1. Hence, its domain would be written like \{x \in \R | x\geq 1\}. 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)
replies: text: Apparently the German article defines a broader concept than the domain of a function. However, with the title "Domain of a function" it is not relevant to discuss expressions such as \sqrt{x-1}. Are there reliable sources in English that define the domain of a term or expression the way you are suggesting? Isheden (talk) 19:11, 17 March 2013 (UTC)
replies: text: The domain of a term or expression is a nonsense if the term does not represent a function. If it represents a function, its domain is that of the function, and no further definition is needed. If the expression represents several functions, then there may be as many different domains. For the above example, if it is considered as a function from the reals into the reals, then the domain is what has been said. If functions from the reals or from the complexes into the complexes are considered, the domain is the whole real line or the whole complex plane. D.Lazard (talk) 09:49, 23 April 2013 (UTC)
replies: text: Possibly the IP user is referring to what is called natural domain in this article: "The natural domain of a formula is the set of values for which it is defined, typically within the reals but sometimes among the integers or complex numbers. For instance the natural domain of square root is the non-negative reals when considered as a real number function." This text passage is quite sloppy, by the way. What exactly is meant by "formula"? Does "square root" refer to \sqrt{x} or rather to the formula f(x) = \sqrt{x}? Is it possible to speak of a natural domain e.g. of the equation \sqrt{x-1}+\sqrt{x+1}=\sqrt{2x+\frac{3}{2}}? Isheden (talk) 13:03, 23 April 2013 (UTC)
replies: text:  Firstly, a formula is a logical assertion. An identity is a formula, but an equation is not. f(x) = \sqrt{x} is not a formula but the definition of the function f (supposing that it has not been defined previously; if it has been defined previously, the meaning depends on the context). The equation that you gives as an example is meaningful on every mathematical structure on which this expression is defined, and only on them. None of these structures is more natural than the others. For example, ax+b may refer to a number, to a polynomial in 3 variables, to a univariate polynomial with a and b as coefficients, to the function of x defined by this polynomial, to a vector and even to a line, if a and b are vectors and x a variable. In other word , one should not make a confusion between the syntax of an expression and its semantic which is provided by the context. When the IP user uses the word term, this refers to the syntax for constructing expressions. As such, there is no domain for a term.  It may have a domain only when interpreted (semantic) implicitly of explicitly as a function. IMO, the notion of natural domain of a formula is WP:OR and also a mathematical nonsense for the above reasons. D.Lazard (talk) 14:07, 23 April 2013 (UTC)
thread_title: Domain of a term?

message: 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)
replies: text: Because the word domain can mean too many other things, even in mathematics.  See domain#Mathematics for a (partial?) list.  However, domain (mathematics) does currently redirect to this article, which muddies the waters a bit. --Trovatore (talk) 19:19, 23 June 2013 (UTC)
thread_title:  Name