Is it really true that Isaac Newton had the concept of limit? I tend to think of that as a 19th-century innovation. Michael Hardy 20:58, 7 Sep 2004 (UTC)
Would like to second that last statement. The defintion given for Infinitesimal includes Newton as using infinitesimals and the idea of the limit wasnt introduced until the 19th century by Karl Weierstrass. Would be nice to keep definitions noncontradictory.
The proposal to merge this with non-standard calculus doesn't make sense. Non-standard calculus did not emerge until the 1950s; this article is about something introduced by Leibniz in the 17th century. Michael Hardy 21:48, 12 Jun 2005 (UTC)
I also find the merge to be a bit inappropriate. Perhaps a disambiguation is a better idea. Based on a Google books search, it seems that the term "infinitesimal calculus" is used both for calculus in the ordinary sense and the sense of non-standard calculus. Sławomir Biały ( talk) 13:19, 2 July 2010 (UTC)
I agree with Michael Hardy and Sławomir Biały, there should be 2 different articles. To my knowledge infinitesimal calculus is usually not associated with non standard analysis as a field, but it is rather used for the "normal" calculus before the analysis rigor of the late 19th/early 20th century and today mostly used as a term for a somewhat less rigorous approach to analysis (like first calculus primers).-- Kmhkmh ( talk) 14:11, 2 July 2010 (UTC)
I agree also. -- Radagast 3 ( talk) 01:01, 3 July 2010 (UTC)
Reprising my comments from
WT:WPM:
Hi, there used to be a parenthetical remark following "standard calculus", clarifying that the standard approach was developed by Cauchy and Weierstrass. The parenthetical remark did not say that infinitesimal calculus was developed by them. What we have today is a pair of approaches that provide rigorous foundation to infinitesimal calculus as envisioned by Newton and Leibniz, namely the approach by Cauchy and Weierstrass on the one hand (called the standard approach), and the much more recent approach of Robinson (non-standard). It would be incorrect to suggest that standard calculus was developed by Newton and Leibniz, as the current version states. Katzmik ( talk) 15:48, 8 January 2009 (UTC)
In mathematical logic, Charles Sanders Peirce had interesting writings about infinitesimals. Secondary literature includes the mathematics historians Joseph W. Dauben, Carolyn Eisele, John L. Bell; c.f. the wider discussions of Peirce's mathematics (and mathematical logic) by the mathematical logicians by Hilary Putnam (e.g. in Peirce's "Reasoning and the Logic of Things") and Jaakko Hintikka (e.g. in "Rule of Reason"). See also:
Thanks, Kiefer.Wolfowitz ( talk) 15:17, 4 July 2010 (UTC)
Trovatore and tkuvho have come to a tentative agreement that IF it can be verified that the term "infinitesimal calculus" can be documented to be used in a historical sense to describe the calculus using infinitesimals prior to Weierstrassian reform, then this page can be turned into a disambiguation page with perhaps three items: (a) calculus; (b) history of calculus; (c) infinitesimal calculus in the sense of Henle's textbook. Tkuvho ( talk) 11:07, 9 July 2010 (UTC)
The 9th edition of the EB has a 68 page article about "Infinitesimal Calculus". WFPM ( talk) 20:03, 15 March 2011 (UTC)
I don't know about the details. It's just in my copy of the 9th EB (R. S. Peale Company, Chicago, 1892. The Infinitesimal Calculus article was managed by Benjamin Wilson, F. R. S., Professor od Mathematics, Trinity College, Dublin. Encyclopardia Britannica Volume 13 (INF - KAN) Pages5 through 72. WFPM ( talk) 11:58, 16 March 2011 (UTC)
Reading this article is like wading through treacle. Please tidy up the language used to make it accessible to more people. Calculus is not a complicated subject if it is taught well. The text in this article may be accurate but if it fails to pass on understanding it is not doing the job an encyclopedia should do.
Best wishes, — Preceding unsigned comment added by 92.20.167.150 ( talk) 21:49, 22 December 2012 (UTC)
This was viewed 15000 times yesterday. Any idea why? xkcd does not seem to be it. Tkuvho ( talk) 15:23, 16 April 2013 (UTC)
The lead says:
This is incorrect. The "part of mathematics concerned with finding tangent lines to curves, areas under curves, minima and maxima, and other geometric and analytic problems" is called calculus.
Infinitesimal calculus is just one approach to calculus.
-- Redaktor ( talk) 14:00, 7 January 2014 (UTC)
Is it really true that Isaac Newton had the concept of limit? I tend to think of that as a 19th-century innovation. Michael Hardy 20:58, 7 Sep 2004 (UTC)
Would like to second that last statement. The defintion given for Infinitesimal includes Newton as using infinitesimals and the idea of the limit wasnt introduced until the 19th century by Karl Weierstrass. Would be nice to keep definitions noncontradictory.
The proposal to merge this with non-standard calculus doesn't make sense. Non-standard calculus did not emerge until the 1950s; this article is about something introduced by Leibniz in the 17th century. Michael Hardy 21:48, 12 Jun 2005 (UTC)
I also find the merge to be a bit inappropriate. Perhaps a disambiguation is a better idea. Based on a Google books search, it seems that the term "infinitesimal calculus" is used both for calculus in the ordinary sense and the sense of non-standard calculus. Sławomir Biały ( talk) 13:19, 2 July 2010 (UTC)
I agree with Michael Hardy and Sławomir Biały, there should be 2 different articles. To my knowledge infinitesimal calculus is usually not associated with non standard analysis as a field, but it is rather used for the "normal" calculus before the analysis rigor of the late 19th/early 20th century and today mostly used as a term for a somewhat less rigorous approach to analysis (like first calculus primers).-- Kmhkmh ( talk) 14:11, 2 July 2010 (UTC)
I agree also. -- Radagast 3 ( talk) 01:01, 3 July 2010 (UTC)
Reprising my comments from
WT:WPM:
Hi, there used to be a parenthetical remark following "standard calculus", clarifying that the standard approach was developed by Cauchy and Weierstrass. The parenthetical remark did not say that infinitesimal calculus was developed by them. What we have today is a pair of approaches that provide rigorous foundation to infinitesimal calculus as envisioned by Newton and Leibniz, namely the approach by Cauchy and Weierstrass on the one hand (called the standard approach), and the much more recent approach of Robinson (non-standard). It would be incorrect to suggest that standard calculus was developed by Newton and Leibniz, as the current version states. Katzmik ( talk) 15:48, 8 January 2009 (UTC)
In mathematical logic, Charles Sanders Peirce had interesting writings about infinitesimals. Secondary literature includes the mathematics historians Joseph W. Dauben, Carolyn Eisele, John L. Bell; c.f. the wider discussions of Peirce's mathematics (and mathematical logic) by the mathematical logicians by Hilary Putnam (e.g. in Peirce's "Reasoning and the Logic of Things") and Jaakko Hintikka (e.g. in "Rule of Reason"). See also:
Thanks, Kiefer.Wolfowitz ( talk) 15:17, 4 July 2010 (UTC)
Trovatore and tkuvho have come to a tentative agreement that IF it can be verified that the term "infinitesimal calculus" can be documented to be used in a historical sense to describe the calculus using infinitesimals prior to Weierstrassian reform, then this page can be turned into a disambiguation page with perhaps three items: (a) calculus; (b) history of calculus; (c) infinitesimal calculus in the sense of Henle's textbook. Tkuvho ( talk) 11:07, 9 July 2010 (UTC)
The 9th edition of the EB has a 68 page article about "Infinitesimal Calculus". WFPM ( talk) 20:03, 15 March 2011 (UTC)
I don't know about the details. It's just in my copy of the 9th EB (R. S. Peale Company, Chicago, 1892. The Infinitesimal Calculus article was managed by Benjamin Wilson, F. R. S., Professor od Mathematics, Trinity College, Dublin. Encyclopardia Britannica Volume 13 (INF - KAN) Pages5 through 72. WFPM ( talk) 11:58, 16 March 2011 (UTC)
Reading this article is like wading through treacle. Please tidy up the language used to make it accessible to more people. Calculus is not a complicated subject if it is taught well. The text in this article may be accurate but if it fails to pass on understanding it is not doing the job an encyclopedia should do.
Best wishes, — Preceding unsigned comment added by 92.20.167.150 ( talk) 21:49, 22 December 2012 (UTC)
This was viewed 15000 times yesterday. Any idea why? xkcd does not seem to be it. Tkuvho ( talk) 15:23, 16 April 2013 (UTC)
The lead says:
This is incorrect. The "part of mathematics concerned with finding tangent lines to curves, areas under curves, minima and maxima, and other geometric and analytic problems" is called calculus.
Infinitesimal calculus is just one approach to calculus.
-- Redaktor ( talk) 14:00, 7 January 2014 (UTC)