# Talk:Calculus

Calculus is a former featured article candidate. Please view the links under Article milestones below to see why the nomination failed. For older candidates, please check the archive.
WikiProject Mathematics (Rated B-class, Top-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 B Class
 Top Importance
Field: Analysis
A vital article.
One of the 500 most frequently viewed mathematics articles.
Wikipedia Version 1.0 Editorial Team / Vital (Rated C-class)
C  This article has been rated as C-Class on the quality scale.

## The history section

Shouldn't the history section have at least some content? I mean, more than the link? --31.45.79.44 (talk) 22:46, 27 February 2012 (UTC)

In the main text we read: "Pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. (André Weil: Number theory. An approach through history. From Hammurapi to Legendre. Birkhauser Boston, Inc., Boston, MA, 1984, ISBN 0-8176-4565-9, p. 28.) " I think that this is misleading. Fermat borrowed from Bachet de Meziriac's Latin translation of Diophantus’ Arithmetika the noun adaequalitas and the verb adaequare where they have a meaning in a completely different context, namely solving a special class of arithmetical problems by the method of false position. Fermat, however, uses those words (and the word adaequabitur) in his method of determining maxima and minima of algebraic terms and of computing tangents of conic sections and other algebraic curves. Fermat’s method is purely algebraic. There is no "infinitesimal error term". Fermat uses two different Latin words for "equals": aequabitur and adaequabitur. He uses aequabitur when the equation describes the identity of two constants or is used to determine a solution or represents a universally valid formula. Example:

${\displaystyle x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})}$.

And he uses the word adaequabitur (${\displaystyle \doteq }$) when the equation describes a relation which is no valid formula. Example (Descartes' folium):

${\displaystyle x^{3}+y^{3}\doteq 3xy}$.

Typical examples are:

${\displaystyle (x+e)(b-x-e)=bx-x^{2}-2ex+be-e^{2}}$

and

${\displaystyle be\doteq 2ex+e^{2}}$.

Equations which describe relations between two variables (x and y, x and e) were unknown to Vieta. So the 21-year-old Fermat felt compelled to introduce a new concept of equality and called it adaequalitas. Later, when he created his analytic geometry he abandoned this special terminology of his younger days. See my paper Barner, Klaus: Fermats <<adaequare>> - und kein Ende? Math. Semesterber. (2011) 58, 13-45, unfortunately written in German. 91.4.83.79 (talk) 17:28, 7 February 2013 (UTC) Klaus Barner (talk) 14:40, 5 February 2013 (UTC)

Very interesting. Is there perhaps a translation of your article online somewhere? Tkuvho (talk) 16:13, 6 February 2013 (UTC)

Unfortunately there is none. The reason is: my German is sophisticated and requires reading between the lines whereas my English ist rather weak. It is no artical about mathematics but about history of mathematics which requires a better command of English than I have. However I feel that I should produce a raw translation and ask a native speaker to improve it. Klaus Barner (talk) 19:09, 10 February 2013 (UTC)

## balance and accuracy concerning controversy concerning origins?

Article says, "When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit." but I understand from the Wikipedia article on the controversy itself (to which this should link) that the controversy evolved many years after Leibniz published his results. Also, the slant of the story itself, as it is told here, seems to favor one side (Newton). — Preceding unsigned comment added by Rentstrike (talkcontribs) 18:25, 28 November 2012 (UTC)

## Capitalization of Calculus

It is my understanding that the formal name for calculus is "The Calculus." While the "The" is generally dropped these days, isn't it still appropriate to capitalize the word Calculus?

"A calculus is a way of calculating, so mathematicians sometimes talk about the 'calculus of logic', the 'calculus of probability', and so on. But all are agreed there is really only one Calculus, pure and simple, and this is spelled with a capital C" (emphasis mine) (Crilly, Tony (2007). 50 Mathematical Ideas You Really Need to Know. London: Quercus Publishing Plc. p. 76, 208. ISBN 1-84724-147-6.)

Interestingly, the index of the book does not capitalize the word.

It would seem seems that we should at least mention the issue of capitalization in the article.

Billiam1185 (talk) 01:02, 4 March 2013 (UTC)

## Why is Leonhard Euler not mentioned ?

To be clear, most who add to the mathematical pages have probable forgotten more than I know about maths (I'm British, so I refuse to call it math). However it couldn't escape my notice that when Google put Leonhard Euler up in a Google doodle and specifically mentioned his historical significance to maths and his important work on infinitesimal calculus, that there is no mention of him whatsoever on the infinitesimal calculus page. Is Google incorrect in its highlighting the importance of Euler? Or is his work on infinitesimal calculus not as important as made out on his Wikipedia page? Either one or the other needs correction?

This is definitely an oversight. Euler should be mentioned both on calculus and infinitesimal calculus. Would you like to contribute a comment there? Tkuvho (talk) 15:05, 20 May 2013 (UTC)

## There should be more technical information

Perhaps more examples on this matter. — Preceding unsigned comment added by Pedrovalle (talkcontribs) 13:11, 20 May 2013 (UTC)

## The introduction should include when and who.

I think there should be something in the introduction about when it was invented and (gulp) who invented it. At the risk of being beaten over the head by all the history revisionists and refactorers out there, I think that should be the 17th century, Newton, and Leibniz. --ChetvornoTALK 00:43, 27 July 2013 (UTC)

## Quote hanging on Newton's edge

The Neumann quote box is hanging on Newton's image edge. Can someone fix it? Tried to, but got rolled-back. Formatting problems. --J. D. Redding 00:11, 28 July 2013 (UTC)

## Really?

Come on, people, let's hold the line for general references. We don't have to give in to the inline-cite extremists, not here. For most aspects of the topic, all our refs are going to say the same thing, probably in almost the same words. Save the inline cites for the stuff that's a little particular, and don't make the reader work through a forest of little blue numbers. --Trovatore (talk) 19:14, 4 December 2013 (UTC)

My take on this... someone comes along and makes some subtle changes. Without inline refs it tends to be pretty hard—if not impossible—to check the sources, at least for me, having not significantly contributed to the article in the past. Inline refs make this much easier. - DVdm (talk) 19:22, 4 December 2013 (UTC)
I resist giving in to citation extremists on non-controversial facts, but having some citations are still useful. For instance, the large Principles section of this article has no citations. If a curious student wanted to learn more about principles of calculus, there are zero pointers to a good source or two on this. It's a flaw. I think the more relaxed citation guidelines in WP:SCICITE would be appropriate here: about one general ref per paragraph. --Mark viking (talk) 20:05, 4 December 2013 (UTC)
I am not a citation extremist. But this article doesn't even meet a one general reference per SECTION standard, much less one general ref per paragraph. Stigmatella aurantiaca (talk) 22:48, 4 December 2013 (UTC)

## Orphaned references in Calculus

I check pages listed in Category:Pages with incorrect ref formatting to try to fix reference errors. One of the things I do is look for content for orphaned references in wikilinked articles. I have found content for some of Calculus's orphans, the problem is that I found more than one version. I can't determine which (if any) is correct for this article, so I am asking for a sentient editor to look it over and copy the correct ref content into this article.

Reference named "almeida":

• From Madhava of Sangamagrama: D F Almeida, J K John and A Zadorozhnyy (2001). "Keralese mathematics: its possible transmission to Europe and the consequential educational implications". Journal of Natural Geometry. 20 (1): 77–104.
• From Indian mathematics: Almeida, D. F.; John, J. K.; Zadorozhnyy, A. (2001), "Keralese Mathematics: Its Possible Transmission to Europe and the Consequential Educational Implications", Journal of Natural Geometry, 20: 77–104.
• From Kerala school of astronomy and mathematics: Almeida, D. F.; John, J. K.; Zadorozhnyy, A. (2001). "Keralese Mathematics: Its Possible Transmission to Europe and the Consequential Educational Implications". Journal of Natural Geometry. 20: 77–104.

I apologize if any of the above are effectively identical; I am just a simple computer program, so I can't determine whether minor differences are significant or not. AnomieBOT 21:02, 11 January 2014 (UTC)

## Merger proposal

CLOSED:

Agree to merger of Infinitesimal calculus into Calculus as per wp:consensus and wp:SNOW. Editor familiar with subject should proceed. Non-Administrative closure-- GenQuest "Talk to Me" 05:31, 16 April 2014 (UTC)

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Request received to merge Infinitesimal calculus into Calculus. User:Unsigned request. Reason= unknown. Please discuss here. GenQuest "Talk to Me" 00:16, 30 March 2014 (UTC)

• Support, with qualifications. I think the main use of the term infinitesimal calculus is simply to mean the calculus; that is, the differential and integral calculus, as opposed to, say, the propositional calculus. So I think infinitesimal calculus should ultimately redirect to calculus. However, whether the content should be merged is a different question. Possibly the content should instead be moved to some title such as infinitesimal methods in the calculus, or else merged into nonstandard analysis, before pointing the redirect at calculus. --Trovatore (talk) 00:35, 30 March 2014 (UTC)
• Update I wrote the above without really looking at the current content of infinitesimal calculus. As it stands, there's actually not that much about infinitesimal methods there, so I'm not sure how much there is to start another article with, or to merge to nonstandard analysis. Still, in principle, I stand by my remarks — for example, it could be (I haven't checked) that the article used to be more about infinitesimal methods, and in that case, that previous content could be used in the way I described. --Trovatore (talk) 00:48, 30 March 2014 (UTC)
• Support. There is not enough material specific to the use of infinitesimals in calculus to warrant an entire article on this topic. All the material presently in the infinitesimal calculus article should be in either the main calculus article or in some closely related article (such as on history, on derivatives or integrals specifically, on non-standard analysis, and so on). Ozob (talk) 02:01, 30 March 2014 (UTC)
• Comment Even if there is enough material for such an article, I don't think infinitesimal calculus is the right name for it. Sorry to be picky about it when we're on the same "side", but I really think the point to stay focused on is, where should the search term infinitesimal calculus point? And in accordance with the "common name" principle, I think that term is more used for the integral and differential calculus (regardless of foundations) than it is for the use of infinitesimals in the foundations of calculus. --Trovatore (talk) 03:45, 30 March 2014 (UTC)
• I think infinitesimal calculus should point to calculus. At this point I think that's what the term refers to; saying "infinitesimal calculus" distinguishes differential and integral calculus (considered together) from, say, propositional calculus. To me it also carries a hint of infinitesimal foundations; maybe they're Newtonian or Leibnizian instead of non-standard analysis, but regardless the term itself suggests that infinitesimals make an appearance in the theory somehow. Ozob (talk) 06:36, 30 March 2014 (UTC)
• Support. Theo (Talk) 10:00, 1 April 2014 (UTC)
• Support As far as I know as a math student with no background in history of math, calculus is essentially a shorthand for infinitesimal calculus. -- Taku (talk) 17:20, 1 April 2014 (UTC)
• Support I think infinitesimal calculus should be merged into calculus, with the redirect also pointing to calculus as the most common usage of the term. The infinitesimal calculus article is mostly redundant with calculus article, except for the "Non-standard calculus" and "Smooth infinitesimal analysis" sections--those could be usefully merged into the Calculus#Limits and infinitesimals section, which doesn't even mention the Non-standard calculus article. --Mark viking (talk) 17:38, 1 April 2014 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

I have undone this edit. It is based on 4 sources, all of which i.m.o. unreliable:

• source [1]: "Categories:Types, School Work, Essays & Theses"
• source [2]: wp:primary self published website by Luke Mastin. Who is Luke Mastin?
• source [3] gives the view of one author, George Gheverghese Joseph, "on a mission to reclaim :India’s pride of place in the world of mathematics." Seems not sufficiently notable to be mentioned here.
• source [4] is wp:circular: "Based on materials from: Wikipedia."

Comments? - DVdm (talk) 10:47, 22 February 2015 (UTC)

Regarding the third source (the Telegraph article), please read beyond the first sentence. George Gheverghese Joseph is an "emeritus professor at Manchester University in the UK" who was "awarded a Royal Society Visiting Fellowship". You can read more about him and his arguments here. Why is Joseph "not sufficiently notable"? Exactly what are your criteria for notability? — Preceding unsigned comment added by 71.106.229.93 (talk) 15:45, 22 February 2015 (UTC)
Are there scholarly secondary sources who cite Joseph? See wp:secondary sources. - DVdm (talk) 15:49, 22 February 2015 (UTC)
Princeton University Press published Joseph's book "The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition)" wherein he makes the arguments cited, and two positive reviews from New Scientist and Times Literary Supplement appear on the PUP website: http://press.princeton.edu/titles/9308.html His scholarly credentials are bona fide: http://www.sagepub.com/authorDetails.nav?contribId=649701 ~~~~ — Preceding unsigned comment added by 71.106.229.93 (talkcontribs) 16:02, 22 February 2015 (UTC)
Just the four tildes, without the nowiki-tags please (~~~~). Thanks.
Yes, but that is a wp:primary source. We need other scholar sources who cite the book. Such sources would establish notability. - DVdm (talk) 16:19, 22 February 2015 (UTC)
From the Wikipedia article on Secondary source: "In scholarship, a secondary source is a document or recording that relates or discusses information originally presented elsewhere. A secondary source contrasts with a primary source, which is an original source of the information being discussed; a primary source can be a person with direct knowledge of a situation, or a document created by such a person. However, as discussed in detail in the section below on classification, deciding how to classify a source is not always an obvious decision. Secondary sources involve generalization, analysis, synthesis, interpretation, or evaluation of the original information. Primary and secondary are relative terms, and some sources may be classified as primary or secondary, depending on how it is used." Princeton University Press and the reviewers at New Scientist and Times Literary Supplement would seem to agree that Joseph's scholarly credentials are unassailable; and his book published in 2010 contains "generalization, analysis, synthesis, interpretation, or evaluation of the original information" pertaining to events of the fourteenth and fifteenth centuries.
Has the citing by other scholarly sources been verified for other works cited on this page, such as those of Katz and Zill? Have their works been published by Ivy League universities? Where might we find Wikipedia's rules for what sources are acceptable and which ones are not? Too many articles on Wikipedia are treated as the private fiefdoms of their self-appointed guardians of correctness, and I've seen excellent scholarship repeatedly censored by such individuals who elsewhere in the same given article fail to abide by the "rules" they invent to set the bar far higher for facts and/or interpretations that they dislike. 71.106.229.93 (talk) 16:55, 22 February 2015 (UTC)
Reviews of a book don't really count as secondary sources for particular statements made in that book. The statements you like to add to the article should be found in other articles or books—preferably not newpapers—, referring to the primary source in question. If other poor or unacceptable sourcing has taken place here, perhaps remedial action should be taken, but it certainly does not warrant addition of more such content—see wp:otherstuffexists. - DVdm (talk) 17:52, 22 February 2015 (UTC)
I asked you specific questions, viz.: (i) Exactly what are your criteria for notability? (ii) Has the citing by other scholarly sources been verified for other works cited on this page, such as those of Katz and Zill? (iii) Have their works been published by Ivy League universities (as Joseph's work has)? (iv) Where might we find Wikipedia's rules for what sources are acceptable and which ones are not? 71.106.229.93 (talk) 18:12, 22 February 2015 (UTC)
George Gheverghese Joseph's book makes arguments in the general direction you are interested in, namely examining Indian contribution to the development of the calculus, but I am not convinced by your claim that Joseph "makes the [specific] arguments cited" in your proposed revision. If you can source these and replace some of the dubious references you provided by page numbers in Joseph this may strengthen your case for inclusion. Tkuvho (talk) 08:42, 23 February 2015 (UTC)
Fair enough. My interest is not geographically specific but rather the acknowledgement of contributions by great minds. Joseph's book covers "the deep influence that the Egyptians and Babylonians had on the Greeks, the Arabs' major creative contributions, and the astounding range of successes of the great civilizations of India and China". I will look further and propose material in the future.71.106.229.93 (talk) 16:00, 24 February 2015 (UTC)
Note that the reliability of Joseph is put into question in a detailed review by Jens Høyrup here. Tkuvho (talk) 08:49, 23 February 2015 (UTC)
Re (i) and (iv): see wp:verifiability and wp:consensus. Re (ii) and (iii) see wp:otherstuffexists. - DVdm (talk) 11:36, 23 February 2015 (UTC)
Again, see wp:verifiability and wp:consensus. In a complete sentence: whether the content is notable or not, and whether the sources are reliable or not, is ultimately decided here by consensus on the article talk page. - DVdm (talk) 16:37, 24 February 2015 (UTC)
User 71.106.229.93, your claim that the link to the mathscinet review contains only "basic bibliographic information on Joseph's book" is in error. The review lists numerous inaccuracies, distortions, and tendentiousness in Joseph's book. Tkuvho (talk) 18:32, 24 February 2015 (UTC)
You have linked to a page that only shows basic bibliographic information on Joseph's book and that requires special access including a 'MathSciNet license'. Is this review freely available elsewhere? 71.106.229.93 (talk) 15:26, 25 February 2015 (UTC)

## Ancient History Section

I've removed this from the article's Ancient History section since it should be dealt with here.

{{clarify|post-text=(Why mention this if not relevant? <-Perhaps it is a first/early instance of volume and area calculation, which the paragraph suggests would be the evolutionary antecedent of modern calculus, thus introducing a historical and logical progression, which would seem to be the purpose of this section.)|date=August 2015}}

Should something be added to the article in way of clarifying this point? Bill Cherowitzo (talk) 04:37, 30 August 2015 (UTC)

## dx + Δx or just dx?

A question. Mesmerate (talk) 04:32, 22 November 2015 (UTC)

It is dx+Δx. Mesmerate (talk) 04:36, 22 November 2015 (UTC)

The context for that part of the article is the historical development of calculus through infinitesimals. At that time, dx was used to refer to an infinitesimal change in x. Such a change in x is too small to be represented by a real number. The replacement of infinitesimals by limits of real-valued increments Δx happened over a century later. The revival of infinitesimals by Robinson happened several centuries later, and his concept of infinitesimals was philosophically different from those used by the pioneers of calculus. Ozob (talk) 04:49, 22 November 2015 (UTC)

Sir, the idea is you're taking the limit as it gets really close to zero, and as it gets closer, that is what it gets closer and closer to. As it gets closer and closer, infinitely, it can be considered infinitesimal. Mesmerate (talk) 04:55, 22 November 2015 (UTC)

You are using a post-Weierstrass interpretation of infinitesimals as limits. That is a historical anachronism. It is not at all how Newton and Leibniz saw what they were doing. Ozob (talk) 04:58, 22 November 2015 (UTC)

Please tell me HOW they saw what they were doing? Mesmerate (talk) 05:05, 22 November 2015 (UTC)

The change in x, or Δx, can be defined to include infintely small or infinitely large numbers in its list of possible numbers. It commonly is, and that is partly why i think it is a just fine canidate for being an infinitesimal. Mesmerate (talk) 05:08, 22 November 2015 (UTC)

So, you think infinitesimals cannot be defined using limits? Mesmerate (talk) 05:11, 22 November 2015 (UTC)

For the inventors of calculus, dx (in Leibniz's notation) represented a change in x that was positive, but smaller than any number. This sounds paradoxical because we want to know what kind of thing dx is (it is by definition not a real number). It was just as paradoxical at the time it was introduced; see the article for some history of objections to calculus. Yet calculus seemed to work, so people went about using it. There were still open foundational questions even as calculus developed into a practical discipline. These foundational questions eventually spurred the work of Cauchy, Weierstrass, Riemann, Lebesgue, and so on, who all came much later than Newton and Leibniz and who gave us the definitions of limits, derivatives, and integrals that we use today. It would be historically incorrect to say that the discoverers of calculus understood it in the same way we do. They didn't. (It's also worth noting that the idea that all of mathematics should be rigorously derived from a small set of axioms did not develop until the 19th century, and it really only triumphed with the rise of Bourbaki.) Ozob (talk) 05:17, 22 November 2015 (UTC)

We are talking about modern calculus, where Δx is allowed to approach zero, and where dx is defined as Δx as dx. Mesmerate (talk) 05:25, 22 November 2015 (UTC)

Sorry. Mesmerate (talk) 05:26, 22 November 2015 (UTC)

• where dx is defined as Δx Mesmerate (talk) 05:26, 22 November 2015 (UTC)
The part of the article you edited is specifically about the history of calculus. Modern foundations are discussed in the following paragraph (and in other appropriate articles). Ozob (talk) 05:31, 22 November 2015 (UTC)

No it isn't, check. Mesmerate (talk) 05:35, 22 November 2015 (UTC)

It's under "principals". Mesmerate (talk) 05:37, 22 November 2015 (UTC)

dx and Δx as used in this article are quite different concepts. Letting Δx → 0 is most definitely not the same as simply having an infinitesimal quantity dx. See the hyperreal numbers for a rigorous discussion of the distinction. Any particular Δx is a finite real number. The operation of letting it approach zero does not make it the same as an infinitesimal, which on its own, without taking a limit, is smaller than any positive real number, yet nonzero. Phrases like "As it gets closer and closer, infinitely, it can be considered infinitesimal" are not mathematically rigorous and do not suffice.--Jasper Deng (talk) 06:33, 22 November 2015 (UTC)

I still argue otherwise, I argue in modern calculus dx itself can be considered as the change in x as it approaches 0. Mesmerate (talk) 12:37, 22 November 2015 (UTC)

And I have already clarified that we are talking about modern calculus, "principals" is not a sub heading of "history". Mesmerate (talk) 18:43, 22 November 2015 (UTC)

The meaning of dx depends on the context and the foundations. In modern differentiation, it is just a notational convenience and has no intrinsic meaning. In modern integration, it is a notation for the variable of integration or for a measure. As a differential form, dx stands for the exterior derivative of the identity function xx. In Robinson's theory of infinitesimals, dx is a hyperreal number.
What I think you are proposing is that dx is a notation for "the limit of Δx as Δx → 0." But this is not what you want: limΔx → 0 Δx = 0 for trivial reasons, and you do not want dx = 0. To derive anything useful, you must take the limit of some function of Δx. For example, the derivative is the result of taking the limit as Δx → 0 of the difference quotient (f(x + Δx) - f(x)) / Δx. In the difference quotient, Δx is not infinitesimal; it is just a real number. Taking the limit detects infinitesimal behavior but does not actually require the use of infinitesimals.
If you'd like to learn more about these topics, I suggest Rudin, Principles of Mathematical Analysis. Ozob (talk) 21:21, 22 November 2015 (UTC)

Sorry, nevermind. I read in a text book that the (dy/dx) could be seperated by multyplying by "dy" and as such, it had a page where it said "Who are we to throw around these numbers?" and defined dx as the change in x. I also understand that something getting infinitely cl in all the mess. I admitzero by itself. I still think that delta x equals zero, i just added a small note and got tangled up in it all. I still think something approaching zero still works like an infinitesimal, except for that one case in which it just goes to zero. Sorry i'm a little put of tune in calculus, plus, please tell me if i am right in "It acts like an infinitesimal, except for that one case.". Mesmerate (talk) 23:44, 22 November 2015 (UTC)

Sorry, i mean you can seperate the (dy/dx) by multyplying by dx, not dy. Mesmerate (talk) 23:46, 22 November 2015 (UTC)

Sorry my sentence 2 sentences ago was messed up. Mesmerate (talk) 23:47, 22 November 2015 (UTC)

I meant to say i got caught in it all, and in all cases except for that case "approaching" acts like an infinitesimal. Mesmerate (talk) 23:48, 22 November 2015 (UTC)

Sorry, by "two sentences ago" i meant two comments ago. Mesmerate (talk) 23:50, 22 November 2015 (UTC)

Also, to clarify, i admit i was wrong. I will stop editing that part of the page, and i am sorry for disrupting wikipedia. Mesmerate (talk) 23:53, 22 November 2015 (UTC)

The idea i had in mind was "dx=the change in x", "the change in x can act infinitesimal in most cases", "the change in x is fine, smd should be mentioned." Mesmerate (talk) 23:57, 22 November 2015 (UTC)

Still, i believe that dx in integrals stands for "the change in x" in integrals,as the definition of the integral uses it alot. infact, it used "the change in x" an infinite number of times. and in both case, dx is short hand for "the limit of this using delta x" Mesmerate (talk) 00:00, 23 November 2015 (UTC)

And as such i would like to start a new discussion. I would like to discuss the idea of mentioning that the meaning of "dx" is different across modern and old calculus. Mesmerate (talk) 00:01, 23 November 2015 (UTC)

## Explanation of the change of the meaning to the notation "dx" from meaning infintesimal, to meaning shorthand for the change in x, whether or not x approaches 0.

Read description. Mesmerate (talk) 00:06, 23 November 2015 (UTC)

I believe it is important enough to be mentioned. Is there any consensus? Mesmerate (talk) 00:07, 23 November 2015 (UTC)

It's explained in Leibniz notation. I'd support including that but not more. Also, by the way, please indent your comments (your next comment below should have two colons (::) appended before it, just like this comment has one before it).--Jasper Deng (talk) 04:13, 23 November 2015 (UTC)
The title of this section is misleading. Whether or not x approaches zero has nothing to do with dx and never did. If, for example, we take the limit as x approaches 7, then dx is still the change in x. Rick Norwood (talk) 12:23, 23 November 2015 (UTC)

On one hand, that entire section is historical - there are no infinitesimals in the real line. I would remove both the δx and the dx from that sentence, which is really only trying to say what an infinitesimal is. The symbol dx is not an infinitesimal in modern treatments of calculus. — Carl (CBM · talk) 12:37, 23 November 2015 (UTC)

It's in "principals", not "history". If it is historical, that's a mistake. Mesmerate (talk) 22:53, 24 November 2015 (UTC)

So we should remove the mention of "dx" meaning infinitesimal all together and only say it's just the change in x? I'm fine with that. Mesmerate (talk) 22:56, 24 November 2015 (UTC)

## The h in the limit definition of a differential

What does h stand for in:

${\displaystyle f'=m={\frac {f(a+h)-f(a)}{(a+h)-a}}={\frac {f(a+h)-f(a)}{h}}...?}$

Why don't we explain it in Calculus#Differential_calculus? Warmest Regards, :)—thecurran Speak your mind my past 13:54, 6 December 2015 (UTC)

It is explained in the article: "If h is a number close to zero..." - DVdm (talk) 15:03, 6 December 2015 (UTC)
I think thecurran means "why do we call it h, particularly, and not some other letter?". I don't know the answer to that. If it turns out there's a known and sourceable explanation, do I think we should put it in the article? Maybe. I'd probably have to hear the explanation first. --Trovatore (talk) 20:40, 6 December 2015 (UTC)
When a fellow student asked why h was taken for Planck's constant, our prof said, because all other letters were already taken by that time. Perhaps it's the same in math: a, b, c, d were reserved for constants, e for the exponentials, f and g for functions (and gunctions ), and h was free. I have never seen a comment about it. - DVdm (talk) 21:10, 6 December 2015 (UTC)
The letter 'h' represents a simple exhalation of air, lesser than any of the other vocalizations that shape vowels or define consonants. It is used for Planck's constant because it's the smallest possible articulation of a meaningful utterance.[citation needed] Willondon (talk) 22:36, 6 December 2015 (UTC)
A glottal stop doesn't involve any air at all, but nobody uses the symbol ʔ for a variable. There may be other reasons for that, though. Ozob (talk) 23:52, 6 December 2015 (UTC)

The h used to be a delta x, but at some point someone decided that a two letter symbol might confuse students, and replaced it with h. I think Thomas was the first, at least the first I saw. I think the explanation "h was free" is as good as any. Rick Norwood (talk) 12:24, 7 December 2015 (UTC)

I'm not quite sure what you mean by "used to". This article used to have a Δx? Or authors used to use it? I'm not going to bother to check the history to see about the article. If you mean authors, I imagine that there are authors who still do — as far as I'm aware, there was no meeting held to decide what to do.
My personal take on the question is that using Δx is a suboptimal choice (and to keep this on topic, we should not use Δx in the article) because it invites learners to read too much into it. Δx can be read "the change in x", and in the indicated formula, it's true that it's the change in x. But that isn't necessary for understanding the formula; the formula itself does not ascribe any intensionality to the Δ symbol, or at least no such intensional reading is necessary. Therefore it's better to use a meaningless variable name like h, precisely because it's meaningless, to avoid giving the impression that the meaning is of the essence in the formula. --Trovatore (talk) 22:24, 7 December 2015 (UTC)

## Babylon Tablets Comment

While adding the note for babylonian astronomer clay tablets, some edits were reverted (and perhaps the reversion also reverted.) Assuming good faith, it is wise to allow for 10 minutes from initial edits before removing content and asking for more citations. The citations requested were being adding during the event. I for one, appreciate the watchful eyes keeping track of article improvement. Kyle(talk) 20:03, 29 January 2016 (UTC)

I still think that these two sources [5] and [6] suffer from wp:recentism. These are non-mathematicians reporting about a non-mathematician's recent finding. A proper wp:secondary source would be one from a scholar i.e. a mathematician in a peer reviewed article. After all, this is an math article, not an archeology one. - DVdm (talk) 21:51, 29 January 2016 (UTC)
Even though I'm the person who entered the citation to the New York Times article, I don't have strong feelings about this recent development needing to appear in Wikipedia. I will go with the flow on this one. Isambard Kingdom (talk) 22:00, 29 January 2016 (UTC)
I agree with DVdm. These references are summaries of a single article containing one person's interpretation of some apparently related clay tablets. One needs only recall the checkered history of the interpretation of Plimpton 322 to see that this interpretation may not hold up under the scrutiny of several specialists. When that vetting is done the result will be in reliable secondary sources and we may freely cite these, but until then it should be treated as a viable theory and not as an established fact. Bill Cherowitzo (talk) 05:18, 30 January 2016 (UTC)
Ok, there seems to be no consensus to keep this addition, so I have removed it again ([7]). - DVdm (talk) 09:03, 30 January 2016 (UTC)

## Calculus... "is the mathematical study of change"??

That sounds cute, but it's not correct, or at best it's only correct in some instances. While dx generally represents change in x, that doesn't mean calculus is "the study of change". O-m-g. Someone please rework that intro. 76.208.70.118 (talk) 02:04, 20 August 2016 (UTC)

That someone could be you! Go for it. WP:BOLD! Ozob (talk) 02:53, 20 August 2016 (UTC)