Talk:Difference quotient

message: Regarding the requests for sources, there are several given, including for Newton's attribution, which is given in the derivative and (now added) quotient rule articles. ~Kaimbridge~15:39, 25 July 2007 (UTC)
replies: text: It was a citation request, not a request for links to webpages or citations that may or may not be on other wikipedia articles.  (and I looked at the web page sources - absolutely none of them said "this method is attributed to Newton" or the ilk) If it is attributed to Newton somewhere, cite it.  Here.  I will restore the citation requests you deleted. 198.163.150.8 (talk) 23:53, 18 January 2008 (UTC)
replies: text: The second link you provided is broken (i think you might have cut and paste erroneously).  The first link, which is a fine link with a nice summary, may not fit the wikipedia standards for reference, since it is only a webpage of some  undergraduate at Bath. (i.e. "some random webpage")  Do you have a more authoritative source?  I could make a webpage that says it came from Leibniz, and that should carry no more or less authority than a random undergraduate's. It probably came from Newton, but we should be formally correct about it.  198.163.150.8 (talk) 23:41, 24 January 2008 (UTC)
replies: text: Similar quotients were used by Fermat and Barrow before Newton, and functional notation was missing in Newton's time anyway, so Newton would not have written quotients this way. (See https://www.brainm.com/software/pubs/math/471fermatMT.pdf, https://en.wikipedia.org/wiki/Isaac_Barrow#Calculating_tangents, for example.) The question is not whether Newton "invented" these quotients—he did not—but whether the term "Newton quotient" is standard terminology, where it appears or first appeared, whether (commonly used) competing terminology exists or not, and whether there is a trace of this debate "in the literature". 2A02:1210:5A6B:9600:9839:D2D:41D1:5B1C (talk) 10:15, 1 October 2022 (UTC)

text: The second link I think was on a professor's page, so that one was iffy to begin with (both the cached and original PDF links did work when I posted them).  As for finding a more authoritative source (or accepting it as de facto), you might want to post that citation request to the derivative and quotient rule articles, as they are more heavily edited by (much) more qualified people who may know!  P=)  ~Kaimbridge~15:04, 25 January 2008 (UTC)
replies: text: I seem to remember that the standard Calculus textbooks call it "Newton's Quotient", e.g., George B. Thomas.  But I do not have my copy handy right now.  Certainly it is in Serge Lang, Calculus, and one finds it on the web on google books on page 313 of The Concise Oxford Dictionary of Mathematics
 By Christopher Clapham, James Nicholson.   This does not say Newton invented it, just that it is called the NEwton quotient.98.109.232.157 (talk) 14:02, 4 September 2014 (UTC)
thread_title:  Citation and sources 

message: I was confused by the usage of the word "point".  It took some rereading to understand that whatever is meant by the word in the article, it is not the geometrical sense that I learned in school.  The thing that the article calls a point is what I might call a value of a single variable (which would correspond to a geometrical point in a 1-dimensional geometry), commonly the x-coordinate as eventually mentioned in the article. 207.189.230.42 (talk) 21:40, 17 July 2008 (UTC)
replies: text: Yes many places seem to use the word "point" when the correct term is just "real number". 2A02:1210:5A6B:9600:9839:D2D:41D1:5B1C (talk) 09:48, 1 October 2022 (UTC)
thread_title:  Terminology usage:  Point 

message: === Infinitesimals ===
I see this page was written from a non-standard analysis point of view. I've added the more standard viewpoint at the beginning based on typical college textbooks, but I think the page needs more work throughout. Some1Redirects4You (talk) 09:44, 26 April 2015 (UTC)
replies: text: I agree that this article is a mess.  I had earlier proposed deleting it and replacing it with a redirect to finite difference (which should be expanded if necessary). cffk (talk) 14:39, 26 April 2015 (UTC)
replies: text:  The difference quotient(s) is/are probably notable by itself/themselves, but it seems some of the content of this page (gratuitously?) goes into other things. I'm not sure why the Central difference or the Backward difference are introduced in the lead, for example. They don't appear to play a role in the sequel. Also, I'm not sure from where to source the section of Higher-order difference quotients, which would be germane to this page. It appears the page was largely written (circa 2005) as a personal essay/expose rather than trying to follow some easily identifiable sources. Some1Redirects4You (talk) 11:41, 27 April 2015 (UTC)
replies: text: Now that the article contains standard analysis, and non-standard analysis viewpoints, I find it very confusing. Since the difference quotient is a definition of the derivative that uses limits, I think the standard analysis view is more appropriate. Russphelan (talk) 00:26, 21 May 2015 (UTC)

text: Or, the two approaches should be clearly separated in the article. Otherwise, the meaning of symbols like dx, and dy are ambiguous. In modern real analysis, they can be of finite size. (see differential of a function for information supporting this) In non-standard analysis, they are infinitesimal. Russphelan (talk) 01:51, 21 May 2015 (UTC)
thread_title:  POV check 

message: I see this page was written from a non-standard analysis point of view. I've added the more standard viewpoint at the beginning based on typical college textbooks, but I think the page needs more work throughout. Some1Redirects4You (talk) 09:44, 26 April 2015 (UTC)
replies: text: I agree that this article is a mess.  I had earlier proposed deleting it and replacing it with a redirect to finite difference (which should be expanded if necessary). cffk (talk) 14:39, 26 April 2015 (UTC)
replies: text:  The difference quotient(s) is/are probably notable by itself/themselves, but it seems some of the content of this page (gratuitously?) goes into other things. I'm not sure why the Central difference or the Backward difference are introduced in the lead, for example. They don't appear to play a role in the sequel. Also, I'm not sure from where to source the section of Higher-order difference quotients, which would be germane to this page. It appears the page was largely written (circa 2005) as a personal essay/expose rather than trying to follow some easily identifiable sources. Some1Redirects4You (talk) 11:41, 27 April 2015 (UTC)
replies: text: Now that the article contains standard analysis, and non-standard analysis viewpoints, I find it very confusing. Since the difference quotient is a definition of the derivative that uses limits, I think the standard analysis view is more appropriate. Russphelan (talk) 00:26, 21 May 2015 (UTC)

text: Or, the two approaches should be clearly separated in the article. Otherwise, the meaning of symbols like dx, and dy are ambiguous. In modern real analysis, they can be of finite size. (see differential of a function for information supporting this) In non-standard analysis, they are infinitesimal. Russphelan (talk) 01:51, 21 May 2015 (UTC)
thread_title:  Infinitesimals 

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thread_title:  External links modified