![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | ← | Archive 5 | Archive 6 | Archive 7 | Archive 8 |
The following section has room for improvement if anyone would like to take a look at it: "Limits and infinitesimals Main articles: Limit (mathematics) and Infinitesimal Calculus is usually developed by manipulating very small quantities. Historically, the first method of doing so was by infinitesimals. These are objects which can be treated like numbers but which are, in some sense, "infinitely small". On a number line, these would be locations which are not zero, but which have zero distance from zero. No non-zero number is an infinitesimal, because its distance from zero is positive. Any multiple of an infinitesimal is still infinitely small, in other words, infinitesimals do not satisfy the Archimedean property. From this viewpoint, calculus is a collection of techniques for manipulating infinitesimals. This viewpoint fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals.
In the 19th century, infinitesimals were replaced by limits. Limits describe the value of a function at a certain input in terms of its values at nearby input. They capture small-scale behavior, just like infinitesimals, but use ordinary numbers. From this viewpoint, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits are easy to put on rigorous foundations, and for this reason they are usually considered to be the standard approach to calculus." Katzmik ( talk) 16:03, 15 January 2009 (UTC)
The section "Limits and infinitesimals" had some problems, in my opinion, which I've tried to fix. It stated "On a number line, these would be locations which are not zero, but which have zero distance from zero." This was incorrect. In nonstandard analysis, for example, an infinitesimal does not have zero distance from zero; the uniqueness of zero is a fact that can be expressed in first-order logic, so the transfer principle says that zero is unique on the hyperreals as well. This statement was also sort of a muddle: "No non-zero number is an infinitesimal, because its distance from zero is positive." The mistake is similar to the mistake in the first statement. It seems as though the person who wrote these statements was trying to give clear distinction between reals and infinitesimals, and was also trying to explain why reals can't be infinitesimals. The first question boils down to the Archimedean principle. The second one depends on the foundational framework you're using for the reals, e.g., an axiomatic one that includes an axiom of completeness, or a constructive one such as Dedekind cuts. I've made some edits to try to make this section correct, without making it too technical.-- 76.167.77.165 ( talk) 18:18, 7 March 2009 (UTC)
The article conspicuously avoids the Liebniz notation when it introduces the derivative, and that's a perfectly reasonable choice to make. However, it then uses the Liebniz notation in other places, without explanation. I think the Liebniz notation is so widespread and useful that it really needs to be explained in the article. I'm going to add a little discussion of it.-- 76.167.77.165 ( talk) 18:23, 7 March 2009 (UTC)
I disagree with the quote; "Calculus is a ubiquitous topic in most modern high schools and universities, and mathematicians around the world continue to contribute to its development.[11]" Calculus was rigourized by Baron Augustin-Louis Cauchy by 1828. No history of calculus I can find indicates any further work on calculus. The reference given to Unesco has no info on calculus or its continued development. 70.31.100.40 ( talk) 01:29, 2 November 2009 (UTC)
This article has been edited by a user who is known to have misused sources to unduly promote certain views (see WP:Jagged 85 cleanup). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent.
Please help by viewing the entry for this article shown at the cleanup page, and check the edits to ensure that any claims are valid, and that any references do in fact verify what is claimed. Tobby72 ( talk) 21:42, 24 August 2010 (UTC)
The BBC programme In Our Time presented by Melvyn Bragg has an episode which may be about this subject (if not moving this note to the appropriate talk page earns cookies). You can add it to "External links" by pasting * {{In Our Time|Calculus|b00mrfwq}}. Rich Farmbrough, 03:01, 16 September 2010 (UTC).
I just reverted this edit by Lorynote which added:
My edit summary mention "unsourced". I see that is not correct since the refs do offer some support for the statement (since the refs were on the second sentence I jumped to the conclusion that the only support was Maria Gaetana Agnesi). However, the material definitely should not be in the "Significance" section, and there needs to be consideration of whether the material is WP:DUE (did the book describe as in a text book, or did it develop?). Johnuniq ( talk) 00:29, 4 December 2010 (UTC)
This source says that "her two volume textbook was the first comprehensive textbook on the calculus after L'Hopital's earlier book", so L'Hopital would be more fundamental, yet is not mentioned in the article. The other source says that "it was one of the first and most complete works on finite and infinitesimal analysis.". So there is no support for "Agnesi is credited with writing the first book...", and neither here, whereas this source is "Condensed from "The Pioneering Women Mathematicians" by G.J. Tee in The Mathematical Intelligencer", so not really a reliabe source. The sources do mention the Witch of Agnesi, but that is more on-topic in analytic geometry, not in calculus. DVdm ( talk) 11:10, 4 December 2010 (UTC)
Also note that the first source says in its disclaimer on http://jwilson.coe.uga.edu/ : "The content and opinions expressed on this Web page do not necessarily reflect the views or nor they endorsed by the University of Georgia or the University System of Georgia.". This is someone's personal web site, so It cannot be taken as a wp:reliable source either.
I think it would be okay to use the second source to write this short statement in the article:
{{
cite web}}
: Unknown parameter |month=
ignored (
help)</ref>No details about or picture of Agnesi are needed here. Readers who click the link get all they want. What do the other contributors think about this? DVdm ( talk) 13:42, 4 December 2010 (UTC)
{{
cite web}}
: Unknown parameter |month=
ignored (
help)). The
Witch of Agnesi curve is named after Agnesi, who wrote about it in 1748 in her book Istituzioni Analitiche. (Mac Curves.
"Witch of Agnesi". MacTutor's Famous Curves Index. University of St Andrew. Retrieved 4 December 2010., this citation taken from the Witch article)Picture I'm in favour of. We have Newton and Leibzitz - the fathers of calculus (that sounds odd I know). Agnesi I agree is probably not more notable as a mathematician (as opposed to a female mathematician) than several others who advanced one area of calculus or other, but I think the addition of her picture would possibly attract the interest of more readers, because she is a woman. It's a bit tokenistic I know, but pictures should mho pique the interest, not just decorate the page. Elen of the Roads ( talk) 16:27, 4 December 2010 (UTC)
FYI, there might be no further comments from Lorynote again on this. - DVdm ( talk) 22:55, 4 December 2010 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | ← | Archive 5 | Archive 6 | Archive 7 | Archive 8 |
The comment(s) below were originally left at Talk:Calculus/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Need to address the issues of clarity and stability raised in the latest GA review.
Geometry guy
23:03, 21 April 2007 (UTC)
Uprated to B+, but some of the exposition is still too advanced, and the recent changes need to be integrated more smoothly. Geometry guy 22:05, 28 May 2007 (UTC) == Benchmark of technical writing == I have been reading math and engineering material on Wikipedia for about five years. This is the first time that I have felt I needed to make a comment on an article: This is the best-written article I have ever read, without contest. The pace and rigor of the article is ideal for a person who has some general inclination in mathematics but who may not be authoritative on the subject. In my opinion, this is exactly the scope at which technical material needs to be written. Very well done. Excellent work. Daniel.sparks ( talk) 23:50, 29 April 2012 (UTC) |
Last edited at 23:50, 29 April 2012 (UTC). Substituted at 20:17, 2 May 2016 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | ← | Archive 5 | Archive 6 | Archive 7 | Archive 8 |
The following section has room for improvement if anyone would like to take a look at it: "Limits and infinitesimals Main articles: Limit (mathematics) and Infinitesimal Calculus is usually developed by manipulating very small quantities. Historically, the first method of doing so was by infinitesimals. These are objects which can be treated like numbers but which are, in some sense, "infinitely small". On a number line, these would be locations which are not zero, but which have zero distance from zero. No non-zero number is an infinitesimal, because its distance from zero is positive. Any multiple of an infinitesimal is still infinitely small, in other words, infinitesimals do not satisfy the Archimedean property. From this viewpoint, calculus is a collection of techniques for manipulating infinitesimals. This viewpoint fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals.
In the 19th century, infinitesimals were replaced by limits. Limits describe the value of a function at a certain input in terms of its values at nearby input. They capture small-scale behavior, just like infinitesimals, but use ordinary numbers. From this viewpoint, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits are easy to put on rigorous foundations, and for this reason they are usually considered to be the standard approach to calculus." Katzmik ( talk) 16:03, 15 January 2009 (UTC)
The section "Limits and infinitesimals" had some problems, in my opinion, which I've tried to fix. It stated "On a number line, these would be locations which are not zero, but which have zero distance from zero." This was incorrect. In nonstandard analysis, for example, an infinitesimal does not have zero distance from zero; the uniqueness of zero is a fact that can be expressed in first-order logic, so the transfer principle says that zero is unique on the hyperreals as well. This statement was also sort of a muddle: "No non-zero number is an infinitesimal, because its distance from zero is positive." The mistake is similar to the mistake in the first statement. It seems as though the person who wrote these statements was trying to give clear distinction between reals and infinitesimals, and was also trying to explain why reals can't be infinitesimals. The first question boils down to the Archimedean principle. The second one depends on the foundational framework you're using for the reals, e.g., an axiomatic one that includes an axiom of completeness, or a constructive one such as Dedekind cuts. I've made some edits to try to make this section correct, without making it too technical.-- 76.167.77.165 ( talk) 18:18, 7 March 2009 (UTC)
The article conspicuously avoids the Liebniz notation when it introduces the derivative, and that's a perfectly reasonable choice to make. However, it then uses the Liebniz notation in other places, without explanation. I think the Liebniz notation is so widespread and useful that it really needs to be explained in the article. I'm going to add a little discussion of it.-- 76.167.77.165 ( talk) 18:23, 7 March 2009 (UTC)
I disagree with the quote; "Calculus is a ubiquitous topic in most modern high schools and universities, and mathematicians around the world continue to contribute to its development.[11]" Calculus was rigourized by Baron Augustin-Louis Cauchy by 1828. No history of calculus I can find indicates any further work on calculus. The reference given to Unesco has no info on calculus or its continued development. 70.31.100.40 ( talk) 01:29, 2 November 2009 (UTC)
This article has been edited by a user who is known to have misused sources to unduly promote certain views (see WP:Jagged 85 cleanup). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent.
Please help by viewing the entry for this article shown at the cleanup page, and check the edits to ensure that any claims are valid, and that any references do in fact verify what is claimed. Tobby72 ( talk) 21:42, 24 August 2010 (UTC)
The BBC programme In Our Time presented by Melvyn Bragg has an episode which may be about this subject (if not moving this note to the appropriate talk page earns cookies). You can add it to "External links" by pasting * {{In Our Time|Calculus|b00mrfwq}}. Rich Farmbrough, 03:01, 16 September 2010 (UTC).
I just reverted this edit by Lorynote which added:
My edit summary mention "unsourced". I see that is not correct since the refs do offer some support for the statement (since the refs were on the second sentence I jumped to the conclusion that the only support was Maria Gaetana Agnesi). However, the material definitely should not be in the "Significance" section, and there needs to be consideration of whether the material is WP:DUE (did the book describe as in a text book, or did it develop?). Johnuniq ( talk) 00:29, 4 December 2010 (UTC)
This source says that "her two volume textbook was the first comprehensive textbook on the calculus after L'Hopital's earlier book", so L'Hopital would be more fundamental, yet is not mentioned in the article. The other source says that "it was one of the first and most complete works on finite and infinitesimal analysis.". So there is no support for "Agnesi is credited with writing the first book...", and neither here, whereas this source is "Condensed from "The Pioneering Women Mathematicians" by G.J. Tee in The Mathematical Intelligencer", so not really a reliabe source. The sources do mention the Witch of Agnesi, but that is more on-topic in analytic geometry, not in calculus. DVdm ( talk) 11:10, 4 December 2010 (UTC)
Also note that the first source says in its disclaimer on http://jwilson.coe.uga.edu/ : "The content and opinions expressed on this Web page do not necessarily reflect the views or nor they endorsed by the University of Georgia or the University System of Georgia.". This is someone's personal web site, so It cannot be taken as a wp:reliable source either.
I think it would be okay to use the second source to write this short statement in the article:
{{
cite web}}
: Unknown parameter |month=
ignored (
help)</ref>No details about or picture of Agnesi are needed here. Readers who click the link get all they want. What do the other contributors think about this? DVdm ( talk) 13:42, 4 December 2010 (UTC)
{{
cite web}}
: Unknown parameter |month=
ignored (
help)). The
Witch of Agnesi curve is named after Agnesi, who wrote about it in 1748 in her book Istituzioni Analitiche. (Mac Curves.
"Witch of Agnesi". MacTutor's Famous Curves Index. University of St Andrew. Retrieved 4 December 2010., this citation taken from the Witch article)Picture I'm in favour of. We have Newton and Leibzitz - the fathers of calculus (that sounds odd I know). Agnesi I agree is probably not more notable as a mathematician (as opposed to a female mathematician) than several others who advanced one area of calculus or other, but I think the addition of her picture would possibly attract the interest of more readers, because she is a woman. It's a bit tokenistic I know, but pictures should mho pique the interest, not just decorate the page. Elen of the Roads ( talk) 16:27, 4 December 2010 (UTC)
FYI, there might be no further comments from Lorynote again on this. - DVdm ( talk) 22:55, 4 December 2010 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | ← | Archive 5 | Archive 6 | Archive 7 | Archive 8 |
The comment(s) below were originally left at Talk:Calculus/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Need to address the issues of clarity and stability raised in the latest GA review.
Geometry guy
23:03, 21 April 2007 (UTC)
Uprated to B+, but some of the exposition is still too advanced, and the recent changes need to be integrated more smoothly. Geometry guy 22:05, 28 May 2007 (UTC) == Benchmark of technical writing == I have been reading math and engineering material on Wikipedia for about five years. This is the first time that I have felt I needed to make a comment on an article: This is the best-written article I have ever read, without contest. The pace and rigor of the article is ideal for a person who has some general inclination in mathematics but who may not be authoritative on the subject. In my opinion, this is exactly the scope at which technical material needs to be written. Very well done. Excellent work. Daniel.sparks ( talk) 23:50, 29 April 2012 (UTC) |
Last edited at 23:50, 29 April 2012 (UTC). Substituted at 20:17, 2 May 2016 (UTC)