Ozob

Minor edit to Volume of n-ball

Perhaps I have misunderstood something, I'm not sure why the surface area of a n-sphere would be proportional to r^n as opposed to r^(n-1). I'm new to Wikipedia and apologize for any errors in formatting.Nelumbo1894 (talk) 16:17, 31 October 2015 (UTC)

The n-sphere is an n-dimensional object which naturally lives in R^{n + 1}. So, for example, S¹ is the unit circle in R² and S² is the unit sphere in R³. The area of such a sphere can be proved to be proportional to the nth power of the radius in the same way that the volume of an n-ball is proportional to the nth power of its radius. Specifically, if A_n is that area, then

$A_{n}(R)=\int _{-R}^{R}A_{n-1}({\sqrt {R^{2}-x^{2}}})\,dx$

because slicing Sⁿ with the hyperplane x = x₀ results in a sphere of one lower dimension and radius ${\sqrt {R^{2}-x_{0}^{2}}}$. By induction, a factor of R can be pulled out of the integrand to get

$R^{n-1}\int _{-R}^{R}A_{n-1}({\sqrt {1-x^{2}/R^{2}}})\,dx.$

Perform the substitution t = x / R.

$R^{n-1}\int _{-1}^{1}A_{n-1}({\sqrt {1-t^{2}}})\,R\,dt=R^{n}A_{n}(1),$

precisely as claimed. Ozob (talk) 01:12, 1 November 2015 (UTC)

[1] (Undid revision 1057481292 by Guswen (talk) Unsourced)

Would you kindly take a sheet of paper, a pencil, and a eraser; redo this simple math and make these equations sourced for me? Guswen (talk) 09:29, 28 November 2021 (UTC)

Sorry, I can't help you that easily; proper sourcing for this fact would require publication. See WP:RS. Ozob (talk) 16:42, 28 November 2021 (UTC)

Thank you. I don't question peer-reviewed publications. But in this case this seems unreasonable. There is known $V_{n}(R)={\frac {2\pi }{n}}R^{2}V_{n-2}(R)$ recurrence relation that can be reversed to negative dimensions [2], [3] yielding volumes (and surfaces) of n-balls in negative dimensions. This recurrence relation gives correct value of n-ball volume in (-1) dimension $V_{-1}={\frac {1}{\pi R}}$ starting from $V_{1}=2R$ [4] so it must be valid for the remaining negative ns.

Recently my preprint [5] has been rejected on the grounds of "The author does not explain how these negative dimensional spaces are defined, nor how n-balls look like in these spaces". But I did not invent negative dimensions (perhaps Benoit Mandelbrot did). And the question "how n-balls look like in these spaces is ridiculous. For humans looking like is limited to $-1\leq n\leq 3$. Guswen (talk) 16:45, 29 November 2021 (UTC)

In the linked paper of Mandelbrot, negative dimensions are only possible for random sets (which are, in effect, sets which you construct by choosing points using dice). But once you have fixed a location and radius, there is only one ball. Since there is no randomness, Mandelbrot's theory does not, as far as I can tell, apply to the case you are interested in. I believe the reviewer who rejected your paper would first like you to define what you mean by a negative-dimensional ball—in some manner independent of the formula for its surface area or volume—and to then verify that surface areas and volumes of balls in negative dimensions continue to satisfy the formulas they ought to. If you think this is unreasonable, you can always try submitting to a different journal. Ozob (talk) 04:59, 30 November 2021 (UTC)

True. The concept of the negative dimension contained in the 2nd link [6] is more appropriate. Here negative dimensions are considered dual to positive ones. Positive dimensions correspond to volumes, negative ones to densities. But dimension is just number. Not necessarily natural. Take -1 dimension of an empty set as an example.

Thank you. I'm trying with another journal. Guswen (talk) 14:48, 30 November 2021 (UTC)

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Computational Anatomy

High Ozob. Michael Miller.

I dont think appropriate for anatomists, just like computational linguistics was not really what linguists were about originally. Now there are many computational linguists.

Conncerning making it appropriate for undergraduate mathematicians, what would be required from your point of view.

Thank-you Mim.cis (talk) 18:54, 19 December 2015 (UTC)

The most important thing to remember is that undergraduates don't really know anything yet, so, as much as possible, you have to convey ideas in intuitive terms instead of precise ones. In one sense this is hard, because we're used to writing for other professional mathematicians, and they expect rigor. But in another sense this ought to be easy, because it's rare that we think directly in rigorous terms. E.g., when I think of a manifold, I imagine a smooth surface in R³, not a metrizable topological space with an atlas, because I can picture the former and not the latter. An undergraduate can visualize a smooth surface in R³; he will be flummoxed by a metrizable topological space with an atlas, and without assistance, he will not recognize the former as an instance of the latter.

With that in mind, here is what I think you need to do to get what you've written into Wikipedia. First, the word "anatomy" appears in the article title. It must be absolutely clear how the mathematics is related to anatomy. The surest way to do this is to provide examples. For example, can CA describe a shoulder joint? The beating of the heart? The firing of neurons? There must be some classic examples that led to the current formalism of orbits under diffeomorphism group actions. These should be examined both to give historical perspective and because they place the general framework in context. They don't need a comprehensive treatment (that would be too detailed for Wikipedia's purpose as an encyclopedia), but without them, most readers will have no idea how what you're doing relates to anatomy. Myself, if I didn't know that the subject was anatomy, I would guess that it was actually differential geometry.

Second, because you can't assume that the reader knows anything, you have to be willing to describe things loosely. When you talk to another professional, you can say (for example) "Sobolev space", and your fellow professional will know what you're talking about, even if he's in an entirely different field like combinatorics or algebraic number theory. But the target undergraduate, if he's completed the basic analysis sequence at all, knows little beyond differentiation and integration. So you can't start by saying "Sobolev space". Nor can you start with "Lie bracket", "geodesic", or even "diffeomorphism". You must first give the reader an intuitive picture. Then, once the undergraduate reader has some context, you can go beyond him. The article should progress from easy to hard, from general to precise, and from loose to rigorous.

Third, the article you've written has a large number of topics. From what I can tell, all these topics are appropriate for Wikipedia. But the article is quite large, and if you take the route I described above and include more descriptions and more examples, the article will get even larger. The solution that Wikipedia has adopted is called "summary style" (see WP:SS). A topic that outgrows its article is trimmed to a brief paragraph or two that mentions only some highlights. The remaining material is put into a new article. This new article is more specialized (just as Riemannian geometry is more specialized than smooth manifold) and must be capable of standing alone (you can't say, "notation is the same as in the computational anatomy article", for instance). You've already started on this with some of the subpages you've created (like User:Mim.cis/sandbox/Group-Actions-Manifolds-CA and User:Mim.cis/sandbox/Sobolev-RKHS-CA). If you want Wikipedia to be a really thorough resource for CA, you will have to do this more extensively, and it will be a big project.

Good luck! I'm happy to give more advice if you need it. Ozob (talk) 22:34, 19 December 2015 (UTC)

Response from Michael Miller at Johns Hopkins to CA Review

Ozob, Thank-you so much for the feedback.

OK, I understand I think I can absorb much of the extra extensions that I have added. I will be parsimonious about it so that we try to use sparingly the equations except whennecessary.

Also for the extra backround sections I will examine those and see if they can be minimized as well. I think I understand your comments.

Then I will check it in.

Mim.cis (talk) 16:12, 24 January 2016 (UTC) Michael Miller

FTC Proof

What is "wrong" with the proof? https://en.wiki.x.io/wiki/Fundamental_theorem_of_calculus — Preceding unsigned comment added by OverLordGoldDragon (talk • contribs) 02:55, 5 February 2016 (UTC)

I'll respond on the article talk page. Ozob (talk) 03:40, 5 February 2016 (UTC)

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Draft "Extended mathematical programming"

Hi Ozob,

You reviewed my draft two weeks ago and recommended comprehensive revision. This is the first time I attempted to write a Wikipedia article and the draft was modeled on the Wikipedia article on SAMPL. I request more details about what should be changed. Is it too long? Too much detail? Too many examples? I'd very much appreciate your input on this. Thank you.

Talomar (talk) 22:26, 19 February 2016 (UTC) Feb 19, 2016

Hi Talomar,

There are two major problems. The first is that all Wikipedia articles must meet the general notability guideline. Depending upon the situation, the GNG has been interpreted in many different ways, but it always expresses the basic principle that Wikipedia should not itself be a source for anything. Wikipedia does not do original research, textbook discussions or tutorials, program manuals, or literature reviews; it does encyclopedia articles. In order to show that EMP is notable you will have to find some secondary sources. The article by Ferris et al., "An Extended Mathematical Programming Framework", looks to be a primary source. As far as I can tell, the other citations in the article are not about EMP (but are rather used as examples of EMP's capabilities). Since the article appears to cite no secondary sources at all, it fails to establish the notability of EMP. (To be honest, I feel like the SAMPL article does not establish its notability, either.) It is still possible that EMP is notable, but that needs to be demonstrated.

The second is stylistic. As I said in my review, it sounds like it's been cut-and-pasted from documentation. There's nothing wrong with a dry, formal style; but in its present state, the article doesn't sound encyclopedic, it sounds instructional, and the goal of a Wikipedia is not to instruct. The goal of the article should be to tell the reader what EMP is rather than how to use it. A potential user can always look at documentation or a tutorial. Ozob (talk) 03:14, 20 February 2016 (UTC)

Hi Ozob,

Thank you for your reply, it was very helpful. In the meantime, I found secondary sources that will serve to establish notability and I will rewrite the article. Thanks again. Talomar (talk) 17:33, 7 March 2016 (UTC)

Warning

Your recent editing history at Divergence theorem shows that you are currently engaged in an edit war. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the article's talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See BRD for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.

Being involved in an edit war can result in your being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you don't violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly.

I cleaned it up for you. Links to dab pages are not ok. Next time, put your ego away and take two seconds to just solve the problem with your article, instead of repeatedly, lazily, and unproductively reverting to a version that is even more wrong. And please don't bother replying to me, here or anywhere else, to satisfy your ego further; I won't read it any more than I read your last time-wasting message. If you can't start working with others, you don't belong here. —swpb^T 13:39, 11 May 2016 (UTC)

I am puzzled by the behavior of user:swpb. Why delete the correct message from Ozob? And why blame Ozob being at least equally edit-warring? Boris Tsirelson (talk) 14:30, 11 May 2016 (UTC)

To editor Tsirel: Ozob's behavior is the failure here. He 3RR'd, I did not, unless you want to revise history, or simply lie. Could I have done the fix earlier? Yes, but I wanted the apparent subject-matter expert to do it, so the target could be appropriately chosen. I also wanted to see if Ozob would take any measure of responsibility, or continue to let his ego rule. We saw the result. He can remove the warning as I removed his comment to me (you should be well aware that there is no problem with that, if you're going to start pronouncing on other people's disputes). I just hope he absorbs it first, or he'll have a bad time. As with Ozob, I really don't need any more replies from you. —swpb^T 14:33, 11 May 2016 (UTC)

How do you decide that his ego is the problem and yours is not? Boris Tsirelson (talk) 14:39, 11 May 2016 (UTC)

Oh, my ego probably is a problem. But I can follow rules. When I 3RR, we can talk. Are you really defending Ozob's indefensible actions, or just trying to spread the blame? —swpb^T 14:42, 11 May 2016 (UTC)

Edit war is punishable also in the absence of 3RR violation (see your message above!). Boris Tsirelson (talk) 14:46, 11 May 2016 (UTC)

And I do not see why his actions are more indefensible than yours. No one of the two was polite. Boris Tsirelson (talk) 14:47, 11 May 2016 (UTC)

My goodness, this is not what I expected at all. Swpb, all I wanted was for you to select a correct disambiguation target or to leave an appropriate tag. My usual practice is to read diffs, and when I read yours, I saw "flow (that is, flux) of a vector field through a surface integral". I said, "No way that's right," and reverted. Since you didn't leave an edit summary, I didn't realize the original link was to a disambiguation page, nor did I know you were trying to fix it. I wanted to assume good faith, and I thought you were merely misguided. After all, inserting incorrect links damages the encyclopedia in a much worse way than links to disambiguation pages do: A reader linked to a disambiguation page can search for the correct target, and the link can eventually be repaired; whereas an incorrect link can make it impossible for a reader to find the content they want, and if it's not immediately removed by those watching the page, it's likely to go unnoticed for a long time.

Then you reverted me, and your edit summary told me to clean up your mess. Well, no. I'm not going to clean up your mess. If you can't be bothered to find appropriate link targets, you shouldn't be disambiguating. I quoted this to you on your talk page, and it's still appropriate: "Do not guess how to fix the link; if you have trouble, tag the link with {{disambiguation needed}}." (WP:WPDAB) Your reverts disrupted Wikipedia far more than any link to a disambiguation page ever did. I stand by my actions and advise you to reread WP:COMPETENCE. Ozob (talk) 23:17, 11 May 2016 (UTC)

Right foot

Given a day, I have to say I'm not proud of my reaction to your reverts, and I apologize for my contribution to the escalation. Cleaning up ambiguous links is a "best guess" game with often large numbers of pages to deal with, but that doesn't excuse what followed in this case. Let's assume we both know how we should act, and that we don't always live up to that. We cool? —swpb^T 14:10, 12 May 2016 (UTC)

Yes, maybe this wasn't handled in the best way. Let's do better next time. Ozob (talk) 00:47, 13 May 2016 (UTC)

Semigroup#Identity_and_zero: Identity element

Hello, I don’t understand why you reverted my edit of the following sentence:

If it has both a left identity and a right identity, a semigroup (and indeed magma) has at most one identity element, which is then two-sided.

First, is it not true that any magma has at most one two-sided identity element? If e and f are such elements, then e = ef = f. If it is true of any magma, why restrict the sentence of the article to magmas having both a left identity and a right identity?

Second, is it not true that if a magma has a left identity and a right identity, then there is exactly one two-sided identity element?

1. Let M be a magma.
2. Assume that b is a left identity of M (for all x in M, bx = x).
3. Assume that o is a right identity of M (for all x in M, xo = x).
4. By (3), b = bo.
5. By (2), bo = o.
6. By (4) and (5), b = o.
7. By (3) and (6), b is a right identity of M.
8. By (2) and (7), b is a two-sided identity element of M.

I may misunderstand these things, in which case I would be thankful if you explained them to me. --Anareth (talk) 09:24, 26 August 2016 (UTC)

Both your statements are correct. When I looked at your edit, I misunderstood the article. I've expanded the article so that hopefully it's more clear now; please take a look and make any further edits you deem necessary. Ozob (talk) 14:49, 27 August 2016 (UTC)

Why did you return my edit in Park Geun-hye?

I showed a evidence! 211.200.180.250 (talk) 03:45, 17 November 2016 (UTC)

Your edit violated WP:BLP. Ozob (talk) 03:53, 17 November 2016 (UTC)

I AfD Calculus I

OK. I am not familiar with procedure here. How do I complete the process of AfD-ing my own article?--Samantha9798 (talk) 14:02, 21 November 2016 (UTC)

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Die/Dice in Expected value

In Expected value, the word "die" is used instead of "dice". Even if "This is still correct English and not a typo," what's the point in using "die" instead of "dice"? When the latter is the commonly accepted –and used– word. Fleon11 (talk) 19:22, 26 April 2017 (UTC)

"Dice" is the plural of "die". Saying "a six-sided dice" is like saying "a four legged cows". See [7] and [8]; as well as [9] and [10]. Ozob (talk) 02:42, 27 April 2017 (UTC)

First, thanks for the clarification. I didn't know that "die" is not only a correct term to refer to the device, but it is the only correct term. Thus, it should be accepted as the rightful term to use in Expected value.

However, I note that the general usage of dice instead of die generates a debate contained within the Linguistic prescription. Using "die" would be the prescriptive approach, and using "dice" would be the descriptive approach. Since, as far as I know, there is no recommendation about this matter in Wikipedia:Manual of Style, I guess any of both approaches should be right. But it wouldn't hurt if the Manual of Style commented on using prescriptive or descriptive language. Fleon11 (talk) 23:02, 1 May 2017 (UTC)

MathJax discussion

Hi Ozob, I started a discussion using MathJax on WT:WPM. Judging from your input here, you might be interested. In any case I would appreciate if you could weigh in in the discussion at WT:WPM. Jakob.scholbach (talk) 09:07, 5 June 2017 (UTC)

Ozob, this is Michael Miller who helped edit the Computational Anatomy pages. wikipedia/Computational anatomy

I wanted to thank-you for all your help. I was a neophyte back then. Our field greatly appreciates have the CA pages now. Many of us in the community use it for classes etc...

Is it possible for you to edit the wiki/JHUBME page and improve it. It says the article contains content that is written as an advertisement. It seems to follow the style of the Oxford Department of Computer Science. I dont actually see what aspects of it are an advertisement. Everything on it is historically accurate. I have a conflict of interest of course since I was announced as the Director in July and encouraged the creation of it following on the Oxford page and the Stanford Computer Science pages which are also top of the field departments.

What would be required for the marks to be removed long term. I was saddened at the news on JohnCD who helped our field with the Computational Anatomy articles as did you. warm regards Mim.cis (talk) 19:05, 2 December 2017 (UTC)

I am very, very pleased that the Computational Anatomy pages have been successful. If only other experts would take the time to write such articles! (I suppose that includes me, but I always find excuses...)

I have never previously had any contact with conflict of interest matters on Wikipedia. Because of that, I do not know how I ought to help you. I believe it would be better for you to ask for assistance at WP:COIN. If the editors there are able to identify specific concerns, then I may be able to help.

In particular, to me the article does not read at all like an advertisement. It might be a little enthusiastic at times: "leading to the rise of similar programs nationwide" and "This founding era gave rise to several significant advances" are too lively for Wikipedia, which prefers its prose bloodless and desiccated. But I do not think a reasonable person would mistake those statements for advertisements. You ought to ask the editor who placed that tag on the article; she should be able to identify what about the article concerned her. Ozob (talk) 04:32, 4 December 2017 (UTC)

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Spaces in mathematics: review

Dear colleague, a review of our manuscript v:Spaces in mathematics is just received. You are more than welcome to read and act accordingly (whatever it means). Yours, Boris Tsirelson (talk) 05:54, 5 April 2018 (UTC)

Thank you for Space (mathematics)#Non-commutative geometry! I'll update accordingly the article and my responce to the third review. In addition, it would be nice to have your opinion on Items 32, 33 of that review (be it expressed here, or there, or by email). Boris Tsirelson (talk) 04:46, 8 April 2018 (UTC)

Thanks again. You are like captain Nemo, enigmatic and helpful. I understand that, in spite of your travel, you are able to edit that article yourself. Feel free to restore "an enormous number of interesting schemes" (replaced by me with "many interesting schemes"), and edit whatever you like. As far as I understand, at some instant we should proclaim that our response is completed (and the next move of the referee should start). I have nothing more to edit, thus, the endpoint should be determined by you. Boris Tsirelson (talk) 04:54, 10 April 2018 (UTC)

Seeing your phrase "I have made edits to the corresponding Wikipedia article that I believe address the concerns above" there, I wonder, do you want me to make the same edits there and then proclaim that our response is completed? Or rather, should I wait for you to continue somehow? Boris Tsirelson (talk) 08:00, 14 April 2018 (UTC)

Oh, I see I was not clear: I have never edited Wikiversity before, and I do not know its established protocols. Would it be acceptable to copy the changes from Wikipedia to Wikiversity? Ozob (talk) 14:04, 14 April 2018 (UTC)

Yes, sure. After all, the whole article was copied from Wikipedia to Wikiversity. That is OK, since they both use the same license, permitting any use (if attributed). And (as you surely know) your new sections are also copied (by me) thereto. Wiki Journal of Science gladly accepts texts from Wikipedia in order to improve them and, when appropriate, copy back to Wikipedia. All these Wikimedia projects are sisters... About attribution: did you note the last two phrases of the manuscript there? Boris Tsirelson (talk) 17:22, 14 April 2018 (UTC)

Now completed; thank you. Boris Tsirelson (talk) 07:02, 15 April 2018 (UTC)

Now we have editorial comments; please look "Substantial remarks and suggestions" there. Boris Tsirelson (talk) 15:21, 25 April 2018 (UTC)

"My" sections are now endowed with diagrams; please look. (Notations are explained in "Relations between species of spaces".) If you like to add such diagrams to "your" sections, please give me the needed information: list of nodes, list of arrows. I'll be glad to make the graphics. Boris Tsirelson (talk) 10:23, 28 April 2018 (UTC)

Yes, I would like to add them. I don't know what to put for the non-commutative geometry section because I don't know enough about non-commutative geometry. For the schemes section, can you do something like:

${\begin{matrix}&&{\text{Projective varieties}}&\hookrightarrow &{\text{Projective schemes}}\\&&\downarrow &&\downarrow \\{\text{Affine varieties}}&\hookrightarrow &{\text{Varieties}}&&{\text{Proper schemes}}\\\downarrow &&&\searrow &\downarrow \\{\text{Affine schemes}}&\hookrightarrow &\to &\to &{\text{Schemes}}\\&&&&\downarrow \\&&&&{\text{Algebraic spaces}}\\&&&&\downarrow \\&&&&{\text{Deligne-Mumford stacks}}\\&&&&\downarrow \\&&&&{\text{Artin stacks}}\end{matrix}}$

All the arrows are injections. For the topoi section,

${\begin{matrix}{\text{Topological spaces}}&\leftrightarrow &{\text{Locales}}&\hookrightarrow &{\text{Grothendieck topoi}}&\hookrightarrow &{\text{Elementary topoi}}\end{matrix}}$

Feel free to rearrange the diagrams to make them look better. Thanks! Ozob (talk) 02:38, 29 April 2018 (UTC)

Nice; I'll do.

But, topological spaces and locales, are these quite equivalent? Boris Tsirelson (talk) 04:39, 29 April 2018 (UTC)

No, they are not. There is a functor in each direction which is an equivalence for good spaces. I am not sure how to draw that. Ozob (talk) 04:45, 29 April 2018 (UTC)

For the topoi, I did; please look. Boris Tsirelson (talk) 07:10, 29 April 2018 (UTC)

In addition, I'd like to enclose the two equivalent structures (sober topological spaces, and spatial locales) into a large box, as I did on Fig. 4 (for finite-dim real linear topological, and finite-dim real linear). Do you like this idea? Boris Tsirelson (talk) 07:34, 29 April 2018 (UTC)

Yes, those are very nice. I agree that a large box around sober topological spaces and spatial locales would be good, too. Ozob (talk) 03:35, 2 May 2018 (UTC)

Please see the recent follow-up. Boris Tsirelson (talk) 20:32, 25 May 2018 (UTC)

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Calculus / Chain Rule article / First Example

Hi, I believe you're one of the main contributing authors to the Chain rule article. I believe there's a problem with the example. I believe the physics can only be described with a differential equation rather than with a simple chain-rule model. The First Example states "(f ∘ g)(t) is the atmospheric pressure the skydiver experiences t seconds after his jump". It's not that simple, because the distance fell after t-seconds is a tiny bit less than that given by g(t) due to buoyancy. I'm not confident to fix it myself though, so I thought I'd message you instead.— Preceding unsigned comment added by MathewMunro (talk • contribs) 09:40, 14 February 2021 (UTC)

Please sign all your talk page messages with four tildes (~~~~) — See Help:Using talk pages. Thanks.

Adequately taken care of. - DVdm (talk) 10:24, 14 February 2021 (UTC)

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Lefschetz hyperplane theorem

Hi, in this edit to Lefschetz hyperplane theorem you introduced references to "Milnor 1969", but did not list any such work. If you could supply the missing reference that would be great. DuncanHill (talk) 14:24, 14 October 2023 (UTC)

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Good article reassessment for Vector space

Vector space has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. ~~ AirshipJungleman29 (talk) 03:00, 25 January 2024 (UTC)