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Definition of the limit of a function

In (?, ?)-definition of limit, limit of a function and several other articles, the limit of a function is defined as

Because of the condition I call this definition the "punctured definition".

The definition that I have learnt more than 40 years ago, is the "unpunctured definition"

I never remarked that there were two different definitions that are commonly given, before the recent discussion at Talk:Function of several real variables#Minor edit: Section on continuity and limit.

In French Wikipedia, it is the unpunctured definition that is given. In German Wikipedia, the punctured definition is given first, and later in the article the unpunctured definition is given in a section called (in German) "Newer definition". (The terms "punctured" and "unpunctured" are the translation of the German words that are used for comparing the definitions.)

I guess that the punctured definition is commonly used in US educational mathematics, while the unpunctured one is more commonly used in advanced mathematics. This needs verification.

I have no clear opinion which definition must be chosen for English Wikipedia, but whichever definition is kept, resource readers must be warned that both definitions are commonly used. As this implies to edit several articles, a discussion is needed here for fixing how we must proceed. D.Lazard (talk) 18:37, 25 November 2020 (UTC)

In my experience, the punctured definition is used universally in English. (But I am not an analyst, I cannot speak to what happens beyond the level of undergraduate education.) Both definitions are discussed in one of the articles, see Limit of a function#Deleted versus non-deleted limits where it is asserted (with citation) that punctured limits are "most popular". (Though it's not the issue here, I like "punctured" better than "deleted".) --JBL (talk) 18:43, 25 November 2020 (UTC)
The fact that the limit of a sequence/function can attain a value that is outside the original set of definition is a tremendously important fact at every level of real analysis. For example, how does one define the limit as of a function with the unpunctured definition of a limit? Mathematicians try their best not to treat infinity as a number, so with the punctured definition, it is straightforward. Many questions like this (compactness, closedness, the relationship between limits/continuity for sequences/functions) are much better understood if you remember from the beginning that limits can land outside the set you originally started with. I vote we use the punctured definition, and give an example such as the one above to explain pedagogically the difference between the two approaches in the article. Tazerenix (talk) 19:30, 25 November 2020 (UTC)
@Tazerenix: I think that's a different issue from the one here: if the point at which the limit is being taken is outside of the domain, then [D.Lazard's version of] the punctured and unpunctured definitions agree (see the universal quantifier ). The question here is rather whether (e.g.) the Kronecker delta function has a limit as or not. --JBL (talk) 19:38, 25 November 2020 (UTC)
Right. The punctured definition allows us to compute limits at removable singularities. Does the unpunctured definition essentially require the function to be continuous, or am I jumping the gun? Mgnbar (talk) 20:07, 25 November 2020 (UTC)
@Mgnbar: that's right, in the unpunctured definition, the condition "the limit exists at a point of the domain" means the same as "the function is continuous at that point". (That is the genesis of this discussion, see Talk:Function of several real variables -- it refers to Function_of_several_real_variables#Continuity_and_limit and in particular the sentence If a is in the interior of the domain, the limit exists if and only if the function is continuous at a in that section of the article.) --JBL (talk) 20:42, 25 November 2020 (UTC)
How is one supposed to discuss semi-continuity with the unpunctured definition? Ozob (talk) 16:12, 26 November 2020 (UTC)
@Ozob: Could you expand on what the issue is here? I was hoping someone better qualified than me would answer your question, but here's my understanding of why this may be a non-problem. Looking at the Semi-continuity article, the formal topological definition of upper semi-continuity at x0 involving neighbourhood U isn't affected by switching between the punctured or unpunctured limit definitions, except possibly when f(x0) = -∞. There's a lim sup formulation for metric spaces (hence for Rn) which involves a limit, but lim sup for a function requires a one sided limit for ε>0 (so not punctured), where ε is the half-width of an interval about x0. (Also, though probably irrelevant, the result is identical whether or not the sup is taken over a punctured or an unpunctured interval around x0.) NeilOnWiki (talk) 15:30, 22 December 2020 (UTC)
@NeilOnWiki: Suppose that for and that . This function is upper semi-continuous, and the limit at exists (under the punctured definition). This kind of situation arises naturally, for example, in algebraic geometry (where is the fiber dimension of the blowup of the origin), but it is not even fully describable using the unpunctured definition.
My opinion is that the unpunctured definition is erroneous, and sources that use it are mistaken. I do not even see a reason for articles to discuss the unpunctured definition unless we can find sources stating that it is a common error. Ozob (talk) 16:02, 22 December 2020 (UTC)
Not sure about semicontinuity, but it would be good to pin down why the difference in definitions arises: eg. whether it's down to European vs. U.S. expectations; or recent trends; or if there's a compelling reason for choosing one definition rather than the other. Encyclopædia Britannica online uses the unpunctured version; as does my British-published Collins dictionary of Mathematics. But the Concise Oxford Dictionary of Mathematics (5 ed.) seems to favour the punctured version. Subjectively, the punctured version seems (to me) to introduce a condition that's irrelevant to the intuition that a function has a limit L at c if f(x) becomes more nearly equal to L as x moves increasingly close to c. Why delete c in the formal definition? It seems unnecessary. Under the unpunctured definition, if we need to exclude c (eg. at a singularity), then we can restrict the function domain accordingly. This, in effect, is what we do if we write (which we see in the Filters in topology article). This notation is redundant under the punctured definition, except for emphasis or disambiguation.
Interestingly, JBL's Limit of a function#Deleted versus non-deleted limits link observes that the unpunctured definition interacts more nicely with function composition (my wording). The source for this is several decades more recent (2015) than the multiple sources cited to support that the punctured definition is more popular (latest 1974). Looking at articles more widely in topology, it seemed to me that English resource is surprisingly consistent in preferring the punctured definition (generalised to open sets, neighbourhoods, nets, etc). The non-standard analysis topics may be less consistent, depending on whether or not an article considers 0 to be an infinitesimal (I'm fairly unconfident here).
Incidentally, the punctured definition vacuously implies (I think!) that if c is an isolated point, then any L in the codomain of f (and not just in the image of f) is a limit as x approaches c. The unique unpunctured limit is f(c). The latter seems less perverse -- though it might just be that the example itself is fairly perverse. NeilOnWiki (talk) 20:46, 2 December 2020 (UTC)
I believe that at least in modern English sources, the punctured definition is used almost universally, at all levels of mathematics. Ebony Jackson (talk) 18:29, 5 December 2020 (UTC)
Yes, this is my experience as well. I find the "unpunctured definition" sort of bizarre, frankly. What is the point of taking a limit, if it has to actually be the value of the function at that point? It seems to be entirely redundant with the notion of continuity; it's not clear why you would need both. And it means that you can't, for example, write the definition of derivative as
which is how it is usually presented in calculus classes. (I suppose you could quibble that is not in the natural domain of the right-hand side, but this strikes me as confusing and error-prone.) --Trovatore (talk) 00:14, 13 December 2020 (UTC)
@Trovatore: I think these are persuasive points. Even so, I'd like to stick up for the unpuncturists, as I think that, even if they're a minority, it's a mathematically valid position and one taken in at least some sources. I guess it'd be good to have an idea of how significant a minority they are.
On your first point, continuity isn't completely equivalent to the unpunctured limit existing (only when the point in question is in the function domain), so the unpunctured limit isn't "entirely redundant". To my mind, the unpunctured definition copes less bizarrely for Real valued functions on the Integers f: ZR, where a puncturist could assert that 2x→0 as x→1 (remembering that xZ -- admittedly I can't think why anyone would do this). These arguments may both be down partly to aesthetic preference.
It's a long time since I learnt calculus and I'm not a teacher. My impression is that any tutor using this definition makes resolutely clear in the preamble that h is non-zero, so there's no ambiguity over the domain. NeilOnWiki (talk) 15:23, 13 December 2020 (UTC)
Perhaps this is a matter of taste, but I find the punctured definition more appealing for functions . This definition means that every real number is a limit of at every point. While ambiguity is not usually a desirable property, I think it is natural in vacuous situations like this. It is still the case that such an is continuous. Ozob (talk) 16:14, 22 December 2020 (UTC)

() Thanks, Ozob. Apologies for being so late replying. I agree this ambiguity is logically consistent, though it does also produce what seems like some odd results geometrically. For example, we now have a continuous f where there's a limit but not a unique one (even though R is a Hausdorff space). Hence, we may need to pause before writing that in general a Real-valued function f is continuous at c iff the limit exists and equals f(c), because we might have to choose our phrasing more carefully to account for non-uniqueness if there's a possibility that c is an isolated point (as happens with cZ above). Interestingly, the Net article has a definition of limit with a punctured flavour for a function from a metric space to a topological space, which does ensure uniqueness when the codomain is Hausdorff. It agrees with the punctured ε-δ definition when c is a cluster point (limit point), but not when c is isolated. Instead, in effect it avoids the vacuous condition for an isolated point and implies the limit either doesn't exist or uniquely equals f(c). (As far as I can tell, although it's not developed there, the obvious unpunctured counterpart would be fully consistent with the unpunctured ε-δ definition for both kinds of point.)

I found this a surprisingly interesting question, not least to see how this kind of Wikiepdia discussion is concluded. MOS:MATHS has a section on Mathematical conventions. Would it make sense to add an entry for Limit of a function there? I also wonder whether it might help future editors by adding a summary of some of the less obvious implications of the punctured definition (notably for function composition and isolated points), if this were put forward as the more popular approach. NeilOnWiki (talk) 14:21, 30 December 2020 (UTC)

Hi Everyone: In the absence of cries of "that's a terrible idea", I'm planning to make the edits to MOS:MATHS that I proposed in the previous paragraph, echoing the consensus here regarding the punctured version (and adding a pointer to this conversation on the MOS:MATHS Talk page). It strikes me that it would be a shame if the current conversation disappeared into the ether, especially considering D.Lazard's initial concerns over the plurality of articles and editors. It may take me a week or so to get round to it, so please stall me if my doing so seems inappropriate or somehow premature. NeilOnWiki (talk) 16:33, 13 January 2021 (UTC)

John Milnor's research

On the research section of John Milnor's page there are several paragraphs which, in my view, have nothing to do with Milnor's research. I removed them but they were added back again. Anybody else's input would be welcome Gumshoe2 (talk) 20:08, 26 December 2020 (UTC)

Doesn't seem to be about Milnor's research so much as other peoples research about his conjecture. It could surely be cut down to one or two sentences at most. I'm not sure one should even bother stating the conjecture (I'm sure Milnor has made a great many interesting conjectures, none of which receive such a significant statement on the page, although it does give a good example of the kind of problem Milnor finds interesting), but certainly there doesn't need to be 3 paragraphs afterwards giving a detailed history of other mathematicians resolution of it.Tazerenix (talk) 12:19, 27 December 2020 (UTC)
Yes, at the very least it should be condensed into a summary; as written, it's not suitable for an overview of Milnor's career. XOR'easter (talk) 16:44, 30 December 2020 (UTC)
Ok, I've removed the paragraphs again with reference to discussion here. Gumshoe2 (talk) 18:04, 30 December 2020 (UTC)

Reliability of tertiary sources such as of Encyclopedia of Mathematics

At Function (mathematics) § Injective, surjective and bijective functions, while getting some citations into this previously {{unreferenced section}}, I replaced a statement that a function is injective if and only if the preimage of each element of its codomain contains at most one element with a statement that a function is injective if and only if the preimage of each element of its range contains exactly one element (Special:Diff/999090776/999284001), because the latter statement (and not the former) appears in what I thought seemed like a convenient source, the "Function" article in the Encyclopedia of Mathematics, which WP:WikiProject Mathematics/Reference resources says [s]hould be regarded as a highly reliable source.

D.Lazard, when you reversed this change, saying EOM os a WP:tertiary source and therefore is not considered as a WP:reliable source in such a case (Special:Diff/999286540), what did you mean? I looked through the policy and guideline you linked, but, as far as I see, neither mentions any case in which being a tertiary source makes a source unreliable (unless the source is Wikipedia).

(This seems like more of a general matter than one specific to Function (mathematics), so I hope I may ask the question here rather than at Talk:Function (mathematics).)

--2d37 (talk) 13:40, 9 January 2021 (UTC)

WP:PSTS: Wikipedia articles should be based on reliable, published secondary sources and, to a lesser extent, on tertiary sources and primary sources.

WP:TERTIARY: Policy: Reliable tertiary sources can be helpful in providing broad summaries of topics that involve many primary and secondary sources, and may be helpful in evaluating due weight, especially when primary or secondary sources contradict each other.

So, the use of tertiary sources for specific technical definitions (as it is the case here) is not recommended, and not forbidden, although secondary sources and well known textbooks are preferred. Here there are many available textbooks, and the previous formulation is clearer than the formulation that is alleged to be closer than that of EOM. As both formulations are mathematically equivalent, and one may be confusing, we must keep the clearer one. If a citation would be needed, we would have to find a textbook that uses a closer formulation. However, as a sourced definition has been given in the preceding sentence, and the equivalence of the two formulations must be very easy for every body who understand them, WP:CALC applies, and I agree with your last edit removing EOM reference. D.Lazard (talk) 16:26, 9 January 2021 (UTC)

About the name of X-Pseudoconvex

There are multiple definitions for the domain called pseudoconvex, and each name seems to be called differently depending on the person, but at Wikipedia, I wanted to discuss how to call it. Perhaps the early treatises were written in French (although one option is to choose a name that is commonly used in English), and on this page I found a user whose native language is French. I thought I would consult on this page. thanks!--SilverMatsu (talk) 23:20, 10 January 2021 (UTC)

Do you mean to say domain of holomorphy, (open) pseudoconvex subset and Stein manifolds are all the same thing so resource should pick one term to refer to them all? It is usually a bad idea to try to mess with terminology in Wikipedia; since, for one thing, there are many anonymous editors who edit math articles and we cannot expect them to be aware of some terminological insider convention. It is desirable and is quite achievable to use some consistency within a single article, though. -- Taku (talk) 00:08, 11 January 2021 (UTC)
Thank you for your reply. In a narrower story, I would like to ask if the usage of the names p-pseudoconvex, Levi pseudoconvex, Strongly pseudoconvex, and Cartan pseudoconvex is popular(commonly). I'm not trying to define these in one way. Each of these definitions has its own advantages. These names are ambiguous to myself. thanks!--SilverMatsu (talk) 00:35, 11 January 2021 (UTC)
Ah, I see. Usually in Wikipedia, the best way to approach the problem like this is to pick and follow a standard and *recent* textbook on the subject. For example, in this case, we can follow Demailly, Complex Analytic and Differential Geometry. In Theorem 7.2. it is shown that various notions like strongly psuedoconvex or weakly psuedoconvex are equivalent and that equivalence is used to define the common notion "pseudoconvex". In Wikipedia, we can do the same; i.e., an open subset is pseudoconvex if it satisfies the following equivalent conditions are met. ..... For Levi pseudoconvex, you need (as I understand) a C_2 boundary so we can say if the boundary is C_2, pseudoconvexity can be characterized in the Levi form. (I'm happy to leave the matters to specialists (I am certainly not) but I am also happy to edit the article myself if needed). -- Taku (talk) 04:03, 11 January 2021 (UTC)
Thank you very much! It was very helpful.--SilverMatsu (talk) 06:54, 11 January 2021 (UTC)

By the way, on the wiki, typing \mathscr seems to give an error.--SilverMatsu (talk) 08:10, 11 January 2021 (UTC)

You can see what TeX math fonts are available at Resource: LaTeX symbols#Fonts. There is \mathcal, but no \mathscr. --2d37 (talk) 11:04, 11 January 2021 (UTC)
Thank you for teaching me. I'll try.--SilverMatsu (talk) 11:09, 11 January 2021 (UTC)
Although it is a 1954 paper, I found a paper that can be used as a reference for the name of the pseudoconvex domain. See With reference to this material, Levi Pseudoconvex can be called as it is, and Levi convex (Equivalent conditions 4) may be called Levi strongly-Pseudoconvex. It seems that it can be called strongly pseudoconvex or locally analytical convex, but if we use strong pseudoconvex for the pseudoconvex region defined using the Strictly plurisubharmonic function, or considering the relationship with the pseudoconvex, I'm thinking of calling it Levi strongly-Pseudoconvex. thanks! --SilverMatsu (talk) 07:03, 24 January 2021 (UTC)

Facet theory

Can people here contribute to dealing with the issues raised by the maintenance tags atop the article titled Facet theory? Michael Hardy (talk) 17:54, 12 January 2021 (UTC)

This does not look like mathematics to me. JRSpriggs (talk) 21:29, 12 January 2021 (UTC)
It looks unfixable to me. XOR'easter (talk) 23:04, 12 January 2021 (UTC)
This appears to also have the same issues (with the same creator and topic for the most part) as Guttman scale. Both need a lot of work. -- MarkH21talk 04:47, 13 January 2021 (UTC)

Properties of integers

Please could a number theorist(?) review recent additions by There are a number of plausible claims which may be worth keeping but the text generally seems too detailed for its articles. Certes (talk) 21:28, 14 January 2021 (UTC)

@Certes: They appear wholly unreferenced and unnoteworthy. I couldn't find any references for these claims from a quick search either. -- MarkH21talk 21:35, 14 January 2021 (UTC)
Is 2 the only prime cake number? It's the only one up to 10,000 but that's hardly a rigorous proof. This seems a simple enough conjecture to have a proof or counter-example or prize on offer, and I can find none of those. Certes (talk) 22:14, 14 January 2021 (UTC)
I have no idea! There isn't much literature on the topic, and I haven't found a reference for that fact either but I wouldn't be surprised if it's out there somewhere. -- MarkH21talk 22:31, 14 January 2021 (UTC)
Oddly enough I'd searched for the cake proof in Yaglom & Yaglom, which you just cited for a different claim, but couldn't find anything relevant. Certes (talk) 22:37, 14 January 2021 (UTC)
Here's a quick and easy proof that just came to mind: is always divisible by 6, since is always even and is divisible by 3 when while is divisible by 3 when . The two factors are also each larger than 6 when n > 5, so has two nontrivial integer factors for n > 5.
Technically, the above is OR. I don't think it's worth me putting this anywhere to circumvent that though. -- MarkH21talk 22:52, 14 January 2021 (UTC)
Thanks; at least it's verifiable in the mathematical rather than the WP:V sense. I was halfway there but my maths is rusty. If we leave the {{cn}} then someone may find that in a book somewhere. Certes (talk) 23:01, 14 January 2021 (UTC)
Yaglom (Vol I, solution 45a) states that the differences are the 2D Lazy caterer's sequence (and uses the fact to derive the formula for the nth 3D cake number), so that may be sufficient proof of that assertion. Certes (talk) 00:13, 15 January 2021 (UTC)
Ah, thanks. Adding the citation now! -- MarkH21talk 00:17, 15 January 2021 (UTC)

Delete "intersection" page?

Hello! I believe we should delete/merge the current intersection page. It should turn into a disambiguation page between intersection (set theory) and intersection (Euclidean geometry).

As it stands, I don't think a "general" intersection page is useful or necessary.

To my understanding, something is either a geometric intersection (so can go to intersection (Euclidean geometry)) or a set theory intersection (and can go to intersection (set theory)). Or maybe someone is looking for intersection theory. I think Intersection should turn into a disambiguation page. Otherwise, what should the "broad" page for intersection be? IMO all it would be is a description of Euclidean or set theory intersections. I don't know what reliable independent sources we could cite that give a broad explanation of both and more.

What do you think? Should we keep intersection? If so, what should we put there? Turn it into a disambiguation page?

I also started a discussion on the intersection (set theory) page.

I think it should be noted that:

And if it is agreed not to change anything, at the very least I think intersection (set theory) needs a hat possibly directing to intersection (Euclidean geometry) or Intersection (disambiguation) and visa versa IllQuill (talk) 06:28, 16 January 2021 (UTC)

I agree that things must change, but I disagree with the proposed changes. IMO, the three article must be merged into a single article called intersection or intersection (mathematics). In fact, in modern mathematics, intersections are almost alway set-theoretical intersections. The only case where intersections are not set-theoretic, are the versions of incidence geometry where a line is not the set of its points. This is very marginal and could be treated in a section "In incidence geometry". This section could be rather short and shoud mainly explain that the two concepts of intersection are essentially the same even if they differ formally. D.Lazard (talk) 12:05, 16 January 2021 (UTC)
While that may be true conceptually, I think there's a very big difference in the set theoretic and geometric article perspectives: the latter is presenting methods for determining the set of points of intersection, hence equations of lines and curves, vectors, etc. The readership of the two articles themselves will also likely have different backgrounds and concerns. Incidentally, Intersection (set theory) as-is nicely complements the article Union (set theory). NeilOnWiki (talk) 14:07, 16 January 2021 (UTC)
Having one article called Intersection (mathematics) makes the most sense to me. It's the simple approach, and I like simple. Too often, we have lots of little articles that each carry a piece of a topic, and the pieces might overlap, telling the same story with contradictory notations -- the inevitable consequence of editors independently adding what they feel like when and where they feel like it without agreeing on a curriculum first. So, every now and then we have to come through and reorganize. Such is life on a wiki! There's nothing wrong with having multiple perspectives in one article, particularly when displaying those perspectives together allows them to illuminate each other. Intersection (set theory) can always redirect to the proper section of the merged article. XOR'easter (talk) 17:03, 16 January 2021 (UTC)
I very much agree the general observation that "Too often, we have lots of little articles that each carry a piece of a topic, and the pieces might overlap, telling the same story with contradictory notations ... So, every now and then we have to come through and reorganize." But, in this particular case, Intersection (set theory) and Intersection (Euclidean geometry) are about very different aspects with no obvious overlap in content beyond the word intersection. The content in the geometry one is mainly vector algebra and solving simultaneous equations. These are applied mathematical techniques where a knowledge of set theory is irrelevant: eg. there's no mention of the word set even when any equation has multiple solutions, nor is there a need to. NeilOnWiki (talk) 19:32, 16 January 2021 (UTC)
I agree with D.Lazard and XOR'easter that we should rename the page Intersection (set theory) as Intersection (mathematics) and include the page Intersection (Euclidean geometry) in it. The overlap is not just in the use of the word "intersection"; there is just one notion of intersection here and it is applied in different areas of mathematics. What is the meaning of "intersection" in Euclidean geometry, if not the notion of intersection that is used throughout mathematics? If you disagree with combining the pages, do you think we should also have separate pages for Intersection (group theory) and Intersection (linear algebra) and ..., with one disambiguation page to rule them all, given that the methods for computing intersections in the different areas of mathematics may be different? To me, having all those separate pages would seem ridiculous. Ebony Jackson (talk) 21:15, 16 January 2021 (UTC)
It is possible to treat geometric lines as first-class objects that are not merely sets of points, and to define intersections of lines as an operation that is not merely intersection of sets of points. But it is not necessary to do so, and I don't see the point in doing so in our main intersection article. I agree that geometric intersections should be covered there, as a special case of set-theoretic intersections. --David Eppstein (talk) 21:38, 16 January 2021 (UTC)
Just chiming in to say that intersections in Algebraic Geometry and very much not set-theoretic, and a great deal of effort in intersection theory is made to understand them in terms of the more intuitive Euclidean intersection picture. This may be relevant when writing/updating the intersection article. Tazerenix (talk) 22:17, 16 January 2021 (UTC)
@David Eppstein: Yes, that is possible. If that is to be mentioned, perhaps it could be done in a "Variants" section of the page (or omitted from this page entirely, as you suggest).
@Tazerenix: Well, most of the time in algebraic geometry when one speaks of the intersection of two varieties, one does mean the intersection of the sets. Even if one is thinking scheme-theoretically, the underlying set is the set-theoretic intersection, and also the functor of points of the scheme-theoretic intersection is the functor whose values are the (set-theoretic) intersections of the values of the functor of points of the two subschemes being intersected. I suppose that you are thinking of the more sophisticated but less common kind of intersection, when one is working in the Chow group or the like, when the intersections are not proper. Anyway, sorry for going off-topic! This shouldn't affect the outcome of the merging discussion. Ebony Jackson (talk) 01:50, 17 January 2021 (UTC)
There are other geometrical aspects of intersections that don't fall into Euclidean Geometry. When studying Immersion (mathematics) the set of self-intersections of the map is of interest, but there is no requirement for either the source or target to be Euclidean. This would point to a wider intersection (mathematics) article.--Salix alba (talk): 06:55, 17 January 2021 (UTC)
Yes, the title does raise a few questions. Looking at its sources, I vaguely wonder if it should have been named Intersection (Computational geometry). But more fundamentally I wonder if we're concentrating too much on rarefied mathematical questions here and need to think more broadly about the encyclopaedia and its users. There's already a more general Intersection (disambiguation) page so in answer to the original question I'm unsure if we'd need a specifically mathematical one. As may be obvious, I'm very much against merging Intersection (set theory) into Intersection (mathematics) — which currently feels a bit of a lonely position. We need (I think) to consider what role is played by each article in disseminating mathematical information, what kind of readership will benefit from it, their background and prior knowledge, their aims and motivation. What's the role of Intersection (set theory)? It looks to me like it's there to explain a concept in (mostly naive) set theory at a fairly introductory level that's accessible to a wide readership. It has issues (not least in nullary intersection), but seems a fairly coherent, reasonably well-defined page if seen in that light, and one which nicely complements the Union (set theory) article. My fear is that we're proposing to turn it into something less accessible and less valuable if we try to merge it into a catch-all page in the way we're arguing. NeilOnWiki (talk) 09:38, 18 January 2021 (UTC)
+1 re: accessibility. --JBL (talk) 14:31, 18 January 2021 (UTC)
Yes, accessibility is important. I think accessibility and merging are not incompatible. An Intersection (mathematics) article could start with an elementary discussion of intersection of sets, and then later sections could mention how intersections in elementary geometry are calculated. If more advanced topics such as "scheme-theoretic intersection" are mentioned at all (and it's not clear that they should be), then they should appear only as remarks towards the end of the article. Ebony Jackson (talk) 17:23, 18 January 2021 (UTC) Resource: WikiProject Physics/Contest

Over at WT:PHYS, we decided to try a bit of an article improvement drive. As there might be an overlap of interest, I figured I'd also post a notice here. XOR'easter (talk) 16:55, 18 January 2021 (UTC)

I think that complex analysis is applicable to this contest. This page points out that there is a lack of explanation from a physics perspective, and this competition may improve it. However, since this competition is focused on physics, the improvement evaluated will be from the perspective of physics, which may complicate the evaluation. Page views are 16,786. --SilverMatsu (talk) 05:12, 19 January 2021 (UTC)

I'm going to change the page name of Hartogs's Theorem

I'm thinking of moving to Hartogs's theorem on separate holomorphicity. Also, looking at Talk:Hartogs's theorem, it seems that the maths rating template is not used. --SilverMatsu (talk) 11:52, 20 January 2021 (UTC)

About the rating template, anyone (e.g., you) is free to add it at any time. If you do move the article (I don't personally have an opinion), the page Hartogs's theorem should presumably be converted into a disambiguation page, pointing at the various targets currently in the note at the top of Hartogs's theorem. --JBL (talk) 13:43, 20 January 2021 (UTC)
I have fixed the hatnote of the article for using a standard format and removing a duplicate link. So, there are only two other links. As the theorem on infinite ordinals is clearly not a primary topic, there are only two candidates for being a primary topic. As these two Hartogs's theorems belong to the same theory (of holomorphic functions of several variables), the primary topic is certainly clear for the specialists. So, per WP:ONEOTHER a dab page seems unneeded.
I have no opinion on the move, but if it is done, the hatnote {{about}} must be replaced by a template {{redirect}}. D.Lazard (talk) 14:48, 20 January 2021 (UTC)
Huh? How is it "clear" that the ordinal theorem is "not a primary topic"? I don't think that's clear at all. --Trovatore (talk) 17:38, 20 January 2021 (UTC)
It is clear because of the size of the interested audience: complex analysis and these Hartogs's theorems are used in many areas of mathematics and physics, while, as far as I know, the properties of transfinite ordinals that are considered here are rarely used outside advanced set theory. D.Lazard (talk) 18:14, 20 January 2021 (UTC)
It's a really pretty, simple, and fundamental construction, from the early days of set theory. Everyone should really know it. The complex-analysis result is more a technical thing from deeper in the bowels of the subject.
That said, it's probably true that hardly anyone refers to the existence of the Hartogs number as "Hartogs' theorem". --Trovatore (talk) 19:17, 20 January 2021 (UTC)
Thank you for improving Hartogs's theorem. I checked the page that links to Hartogs's theorem, but it seems a bit confusing. Looking at the Friedrich Hartogs page, it seems that it is linked to the Hartogs number by writing Hartogs's theorem. Even for several complex variables, the link that explains that the continuity of the condition that the function becomes holomorphic can be derived from the separate holomorphicity was previously the Hartogs extension theorem, and the name was confused. This was the reason for trying to clarify this name.--SilverMatsu (talk) 06:04, 21 January 2021 (UTC)
@Kpgjhpjm: Thank you for the message. Please check out the discussion here.--SilverMatsu (talk) 07:14, 21 January 2021 (UTC)
@SilverMatsu:, Thanks for the ping , You may convert the page into a dab page as mentioned above. Kpgjhpjm 07:34, 21 January 2021 (UTC)

Requested move 20 January 2021

- WP:COMMONNAME says that names used most frequently in reliable sources should be used on resource when a topic has multiple names or a name can be used for multiple topics. When I Google "Stokes' theorem" and search through sources like e-textbooks, university websites, and mathematical databases (which are presumably reliable for mathematical topics), they overwhelmingly refer to the "specialized" case. And when I search "Generalized Stokes theorem," there are plenty of hits for that case. On the other hand, when I search "Kelvin-Stokes theorem," there ARE reliable sources that use that name, but it's not the most commonly known or the most likely to be searched by someone wanting to know more about this case. While few people know enough mathematics to describe the "specialized" Stokes' theorem, even fewer would be familiar with the more general case. I know that when I went to Stokes' theorem on Wikipedia, I was expecting the vector-calculus case. In short, I think this move would make the articles more useful to the average reader. ChromaNebula (talk) 18:56, 20 January 2021 (UTC)

  • Support: For both versions of the theorem, the most common name is Stokes' theorem, but yes, more of the people who search for Stokes' theorem are going to be looking for the version in . "Kelvin-Stokes theorem" should be a redirect to the new Stokes' theorem page. The new "Generalized Stokes theorem" page should say in the lead that the more common name for the generalized Stokes theorem is simply "Stokes' theorem". Ebony Jackson (talk) 22:18, 20 January 2021 (UTC)
  • Support: As both the nominator and Ebony Jackson noted, Stokes' theorem is the WP:COMMONNAME for both articles but the is far more common for a non-specialized audience. -- MarkH21talk 22:23, 20 January 2021 (UTC)
  • Comment: An alternative is to move Stokes' theorem -> Generalized Stokes theorem, leave Kelvin-Stokes theorem where it is and create a dab called Stokes' theorem. That works best if neither article is a primary topic for "Stokes' theorem"; I'm not sure whether that is the case. (To me it means , but I'm not a practicing mathematician.) Certes (talk) 00:02, 21 January 2021 (UTC)
    • One could do that, but given that they are two versions of the same theorem, one more general than the other, a DAB does not make so much sense logically, I'd say. Ebony Jackson (talk) 03:12, 21 January 2021 (UTC)
  • Comment: This discussion seems to be in the wrong place. RM discussions are supposed to be placed on the article Talk page of an affected article, not on the Talk page of a WikiProject, according to the instructions at WP:RM. -- BarrelProof (talk) 02:01, 21 January 2021 (UTC)
    • I see your point. I actually asked at the help desk where to take this move discussion, and the staffer there told me to take it here because this is a highly technical topic. Mathematics pages also see so little traffic that a move request there might not generate adequate discussion. ChromaNebula (talk) 02:53, 21 January 2021 (UTC)
  • Support but since "generalized Stokes' theorem" does not seem to be a standard name, I suggest we instead use the title "Stokes' theorem (general version)". -- Taku (talk) 02:14, 21 January 2021 (UTC)
  • Comment: I'm unsure how typical this is, or how conforming, but if I were looking for Stokes' Theorem on resource as a user, then I might expect them both to be listed as Stokes' Theorem with disambiguation in brackets. E.g. I'd know straightaway that Stokes' Theorem (differential forms) was the general one. I'm less sure about the specialised version: maybe Stokes' theorem (classical); or Stokes' Theorem (line integral). NeilOnWiki (talk) 13:38, 21 January 2021 (UTC)
  • Support the two moves as proposed (well, with the extra ' in the second version) -- the vector calculus version is clearly the primary topic here, and its common name is Stokes' theorem. I prefer natural disambiguation (generalized Stokes' theorem) to parenthetical disambiguation; of the parenthetical options, the best mentioned so far is Stokes' Theorem (differential forms). --JBL (talk) 14:16, 21 January 2021 (UTC)
  • Support in agreement with JBL's comment. Did Mr Stokes work on this generalized form or was his theorem only about . Very few people will ever have to deal with the generalized forms. Also, I can't seem to find any sources that call the theorem Kelvin-Stokes' theorem, that's definitely not its most common name. Ponor (talk) 15:54, 21 January 2021 (UTC)
    • According to this history, the basic theorem first appeared in a letter from Kelvin to Stokes, and Stokes put it on an exam for students, and the first published proof was by Hankel. So Stokes was responsible neither for the statement nor the proof. The generalized Stokes' theorem was not stated or proved by Stokes either; it is due to Cartan much later. By the way, the history I cited does use the term generalized Stokes' theorem, and I think some others do too, so it is not unreasonable to use that as a name for a resource article, even if the name used to describe the generalized version is more often just Stokes' theorem. Ebony Jackson (talk) 17:08, 21 January 2021 (UTC)

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