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Linking to youtube?

Could you explain what the issue is with linking to youtube? I went to WP:YOUTUBE and it explains that there is not a blanket ban on youtube links. I can imagine links to youtube can be concerning due to likelihood of copyright violations, as well as spamminess due to people self-promoting their own videos. However, the 3Blue1Brown essence of linear algebra has essentially become the go to video series recommendation that I encounter on forums when people ask for help with understanding linear algebra, so I feel its inclusion is warranted as a valuable learning aid especially given that there are currently no other video resources in that external link section. Thank you for your time. JustOneMore (talk) 22:01, 24 July 2018 (UTC)

The issue with YouTube videos has more to do with reliability than the concerns you have mentioned. There are some YouTube videos given by established authorities for which this is not a concern (hence no blanket ban on these links), but the vast majority do not have this kind of pedigree. Wikipedia is a gateway to reliable secondary sources of information and if that reliability can not be established then the source does not belong on Wikipedia. These videos, when properly done, can be very good pedagogical tools, but Wikipedia is not a textbook, our purpose is not to teach. When Wikipedia puts a source on its pages, it is implied that the information in that source is certified, but who certifies the validity of YouTube videos? --Bill Cherowitzo (talk) 03:27, 25 July 2018 (UTC)

These videos were originally published on Khan Academy, but were migrated over to its creator's youtube channel after they began working full time as a youtube content creator. So if you consider Khan Academy to be reliable enough then that would satisfy the video's reliability. With regards to Wikipedia not being used to teach, WP:ELYES explicitly lists "online textbooks" under "What can normally be linked", and indeed half of the current external links in the Linear Algebra article are to online textbooks. JustOneMore (talk) 05:26, 25 July 2018 (UTC)

You do realize that Khan Academy is not an academy, it is not a credit producing institution and it is not accredited by any accrediting body that I am aware of. They produce useful YouTube videos that may help students and/or instructors and this is good, but that does not make them an authority on the subjects they deal with. So, the short answer is no, I do not consider them to be a reliable source. Textbooks, because they are vetted by the academic community, are considered to be reliable sources and could be used to support statements in an article. Personally, I would not include them in an external links section, as is done in this article, but I am not about to make a one man crusade on this issue, especially since, as I said, they could be used as sources. --Bill Cherowitzo (talk) 20:35, 25 July 2018 (UTC)

Khan academy is an educational non-profit which employs content experts to review their material before publication, a process analogous to how textbooks are vetted by a few content experts hired by their publisher before they are published. Such a process is known to allow errors through, which is why Khan videos have been called out (and corrected) for errors as have many textbooks. For this reason I would not generally consider textbooks to be reliable enough sources for anything with the potential for technical pitfalls (for instance there is a known fake proof of the chainrule that has been floated around textbooks for decades). As far as the actual content of the videos is concerned, however, I believe nothing appears in the video series which does not already appear on related Wikipedia articles. What these videos provide is not a novel way to understand linear algebra, nor is it a deep treatment, but rather a visual presentation of core concepts that cannot be reduplicated via text or still images. For this reason it would seem difficult to justify exclusion of this video series on the basis of the verifiability of its content when analogous material we have already deemed verifiable enough to appear in our articles themselves. I believe if you take the time to watch the videos that you will agree that there does not appear to be anything of concern in them. JustOneMore (talk) 01:05, 26 July 2018 (UTC)

There are several things I can say in response, but primarily, if you want to argue for the inclusion of these videos, the appropriate place to do that is on the Linear algebra talk page. When editors disagree about something we talk it to death and try to come to a consensus on the problem, with many editors able to contribute to the discussion. As to your main points, I am fully aware of errors in textbooks–in over 30 years of using them I have never found one that didn't contain at least one error–but this has nothing to do with whether or not they are considered reliable sources on Wikipedia. Authors are identified, reviews are published, they are examined by screening committees ... these are the things that make them reliable. While I am fully capable of viewing these videos and giving them my personal seal of approval, this is not how Wikipedia operates. Specialized knowledge of its editors is not to be used in that way. We don't evaluate sources, rather we find published authorities who have and report on what they say. This chaffs at times, but it is necessary given the nature of the Wikipedia experiment. --Bill Cherowitzo (talk) 03:19, 26 July 2018 (UTC)

WP-Disruption, Functions and Mbachtold

Currently I am in a somewhat excited mood about -as it appears to me- WP-customary behaviour against editors, not only in the usual realm of those who taste like newbies or not-full-blown professionals, who dare to oppose to reverting their attempts, where Mbachtold belongs to, but mostly because of the deleting and closing of matters belonging to Michael Hardy. I consider it to be beyond me to discuss this matter, I just remark that I already "know" Izno, and that I have seen Admins at work, and -predominantly- that I rather would retain MH in exchange for some of these admins.

Nevertheless, I wouldn't bother you, if it were not for

Your comments are laced with personal attacks, typically a sign of immature frustration, and that puts so many editors off that you are not likely to make any converts.

stated in your "delayed reply" at Talk:function. Disregarding any context I agree to the first part, consider the second to be speculative and needlessly offensive, and bemoan the last part -especially in its setting of newbie vs. editors in good standing- as illustrating a blockheadedness within established editors.

Since I involved myself I report my view. Considering "f is a function of x" as improvable is not a bad thing, reverting Mbachtold for involving "f(x)" neither. Starting to go at war with DeaconVorbis is not an advisable move, but here you can find already at least a relative maximum of drive-away reasons, but similarly, D.Lazard is likely to have a threatening eye (3RR) on the status quo. Reversion of my effort by D. Eppstein may be debatable, too, but I honestly still estimate my suggestion to be a viable compromise, but I am not sufficiently interested in running against walls. By requesting a citation for the longstanding and questionable formulation, Mbachtold is, of course, sort of against divine right, and this almost demands for calling him Randy (linking there is imho a still more subtle offense by an ADMIN - quod licet iovi, ...).

Is it allowed to call this a crossing of Rubicon? The debate about the placement of a citation not backing a statement is just a bitter cherry on this sh*t-cake about a not fully consistent, but widespread formulation, where WP feels no responsibility to right this small wrong. Who "makes converts", and who "drives away" whom?

From my (short) involvement (visit Mbachtold's TP, in case you're interested) I can report that Mbachtold is personally -above low level- interested (call it OR) in this question, so his sources are not really off track, and, imho, he has a point, he did not start "personal attacks", but rather his legitimate aspects were disrupted with WP-routine, and I consider your delayed verdict as part of this disruption, belonging to the same stinky routine that also works against MH.

I regret that this grew so long. In case of courtesy pings being de rigeur above (I'm not sufficiently versed), please, let me know, or provide them in your scope. Purgy (talk) 10:10, 2 September 2018 (UTC)

Hi Purgy. Sorry that you feel that way, but I think that you are simultaneously reading too much and yet not enough into what I had to say. I applaud that you stick up for the newbie versus what you see as a hostile establishment, but your anti-establishment viewpoint is well known and this does not come as a surprise to anyone who has followed your comments over the years. At times it takes some work to get past that and see the value of what you have to say. All in all, I think it is worth the effort. As to my comments to Mbachtold, they were meant to be helpful to a new editor, although harsh. I had read everything he wrote, including the external links, and it was clear to me that he was pushing his own agenda and was going about it in a way that was surely going to create enemies. It was this that evoked David's RANDY remark, and as unfortunate as I think that remark was, it did not come out of the blue. What got me to write my comments had nothing to do with the minor issue of citation (which, as I explained, I actually agree with him) but rather the personal attacks against me and others, and especially Prof. Lazard. I decided to "fight fire with fire", and my comments were deliberately offensive. If he is going to spew this garbage then he needs to experience it on the receiving end. And, by the way, I, like you, support MH and think that there was some shoddy business in that affair. --Bill Cherowitzo (talk) 19:18, 2 September 2018 (UTC)

Edit-war

You currently appear to be engaged in an edit war according to the reverts you have made on Turn (geometry). Users are expected to collaborate with others, to avoid editing disruptively, and to try to reach a consensus, rather than repeatedly undoing other users' edits once it is known that there is a disagreement.

Points to note:

1. Edit warring is disruptive regardless of how many reverts you have made;
2. Do not edit war even if you believe you are right.

If you find yourself in an editing dispute, use the article's talk page to discuss controversial changes and work towards a version that represents consensus among editors. You can post a request for help at an appropriate noticeboard or seek dispute resolution. In some cases, it may be appropriate to request temporary page protection. If you engage in an edit war, you may be blocked from editing.
The editor who uses the pseudonym "JamesBWatson" (talk) 19:09, 18 September 2018 (UTC)

"arctan" vs. "Arctan"

Don't worry, I primarily just came here to say thanks for your support in this capital matter. However, because you mentioned to have a faint(?) memory of a source, substantiating my unsourced habit of capitalizing principal values, I want to deposit the result of some quick and dirty look-up.

1. Table of Arctan X (Natural Bureau of Standards Applied Mathematics Series 26) (bolding mine): I do not assume that a printed table is not confined to principal values.
2. Precalculus Mathematics employs my habit not only for the inverse trigs, but also for the trigs with respectively truncated domains (Sin, Cos, Tan, ...) and their inverse functions (Arcsin, Arccos, Arctan, ...). Not bad, just who needs bijective trigs ... p.226: Since Sine, Cosine and Tangent are one-to-one functions, their inverse functions exist and are defined as ... Arcsine, ...
3. Wolfram.mathworld destroys any hope for consistency by stating Such principal values are sometimes denoted with a capital letter, but also ... notations are sometimes reversed, ... (Spanier and Oldham 1987, p. 333). Under the header "Wolfram Language" the capitalized names are used in a table to refer to the principal branch.

Regarding the complex logarithm, there seems to be a broad agreement on using exactly "Log" for its principal branch. (Who needs this?)

I'm thinking about an authentic language, or wait for some prescribed terminology. Even when I consider the discrimination by capitalizing as really useful, I won't fight against some paper shufflers. Thanks for all your efforts, and have a fine holiday. Purgy (talk) 12:33, 19 September 2018 (UTC)

No problem. Glad to help out. I've been using that convention in my lower level classes for years, so it must have been popular in Precalculus and Calculus texts, as I am sure that I did not make it up. --Bill Cherowitzo (talk) 18:02, 19 September 2018 (UTC)

Ellipse revert

Would you kindly and responsibly explain before you revert?

I have responded to this on the appropriate talk page.--Bill Cherowitzo (talk) 18:39, 25 September 2018 (UTC)

List of numbers and 50.247.108.35

That wasn't trivia, it was vandalism. Mario was added as 4 different numbers.... — Arthur Rubin (talk) 09:14, 18 October 2018 (UTC)

Quite right. I was getting a little fatigued of reverting this so often and slipped up my edit summary. --Bill Cherowitzo (talk) 18:50, 18 October 2018 (UTC)

Inverse proportion square root seems new to you?

Let's discuss Archimedes square root of 3 that was modified to improve the upper and lower limits of pi, once limited to 22/7. Kevin Brown's math pages cites the issue as an unsolved problem, yet he includes the correct approach along with many dead ends.

Fibonacci and Galileo make explicit Archimedes method with respect to the square root of ten , began with (3 + 1/6) square = 10 1/36, and other examples. Improvements to initial guess errors were divided by twice The initial guess, namely

1/36 was divided by 2(3 + 1/6) by inverting and multiplying...Based on the middle term of the binomial theorem, such that, in modern Vulgar fractions

1/36 x 6/38 = 1/228 which meant a second guess

(3 + 1/6 - 1/228) squared was accurate to the square of 1/228

As the 800 bce sulba-sutra estimated the square root of 2 by beginning with

(1 + 5/12) squared = (17/12)(17/12) = 289/144 = 2 + 1/144

Error 1/144 also divided by twice The initial guess, and inverted and multiplied such that

1/144 x 12/34 = 1/408 which meant a second guess

(1 + 1/3 + 1/12 - 1/408) squared was accurate to 1/408 squared

A third guess divided 1/408 by 2 (17/12 - 1/408) was accurate to 11 decimal places 800 years before Heron created a geometric version off this very old unit fraction method to calculate this class of irrational numbers

Milo

Milogardner (talk) 14:12, 21 October 2018 (UTC)

The reason for my revert was that the article was about the sulba sutras and not about improvements to the mathematics that is contained in them. You made no attempt to tie this in to the subject of the article so I considered it to be superfluous. --Bill Cherowitzo (talk) 18:11, 22 October 2018 (UTC)

Conchoid of Dürer

Hi Bill, hope all's well. I had a question about the figure you added in this edit: according to the text, the distance b should be the sum of the lengths of the two legs of the right triangle, but in the figure it is the hypotenuse. Which description is in error? (As is probably obvious, I haven't taken the time to think through the content of the article at all yet.) Thanks, JBL (talk) 19:04, 24 October 2018 (UTC)

I must have been half asleep yesterday, yes you are right, my labeling is incorrect. I also messed up the file names in the gallery, and I'm not sure about the first one (it might just be that the scale is not the same as the others). I will fix these problems either later today or tomorrow. Thanks for the extra pair of eyes on this. --Bill Cherowitzo (talk) 19:21, 24 October 2018 (UTC)

Sure thing -- anything's better than grading ;). At some point I hope to take an hour and actually read through the thing properly. --JBL (talk) 22:15, 24 October 2018 (UTC)

While changes in my personal circumstances made my retirement necessary, in an alternate universe I'd still be teaching—until grading did me in. I've fixed the major error, but introduced a minor one (I've labeled distances with numbers that could be negative). I could redo the whole thing to avoid that appearance, but I'd rather chalk it up to artistic license and leave it alone. If you think I really ought to fix it I will. --Bill Cherowitzo (talk) 22:51, 24 October 2018 (UTC)

Thanks. I don't think the issue you mention is worth fiddling about. (In the diagram in question, both numbers are positive.) --JBL (talk) 00:50, 26 October 2018 (UTC)

Nonagon

Hey there. You reverted my changes at nonagon, and obviously that's fine. WP:BRD But I didn't see anything on the talk page from you. I re-segregated the approximations and called out their (internally consistant) accuracies without putting in any of the other stuff. Could you have a look and let me know if this works for you?

Riventree (talk) 05:23, 1 November 2018 (UTC)

I have responded on the Talk:Nonagon page. --Bill Cherowitzo (talk) 18:41, 1 November 2018 (UTC)

Lead

Hello, sorry if I bother you, but could you please check if the intro of this page sounds natural and fluid? If you're willing to, I thank you very much. Drow (talk) 09:44, 2 November 2018 (UTC)

There is nothing terribly wrong with the lead of that article, but the flow could be improved. I'll make the changes, but feel free to reject them. --Bill Cherowitzo (talk) 17:32, 2 November 2018 (UTC)

Thank you very much. Drow (talk) 09:25, 3 November 2018 (UTC)

Primary reference on Foata's transition lemma

You have reverted an addition that I made to the Foata's transition lemma entry in the article on permutations, stating that "secondary ref. in English is better than primary ref. in French." Well, maybe I agree, but here is my rationale: (i) it's an entry called "Foata's transition lemma," and I believe that it should point to the place where the correspondence was established; (ii) the article on permutations is already full of references to technical papers and advanced books; (iii) the world is a multilingual place, as you might know.

So, as a compromise, I suggest that a reference be given to some textbook (in whatever language) together with the reference to the original derivation, that I located precisely and may be useful to readers of the Wikipedia article. B.t.w., the book by Bóna is not the best place to point a curious reader; i.m.h.o., the presentation of the usefulness of Foata's correspondence at an elementary level is much better in the "baby" R. Sedgewick & P. Flajolet, "An Intro. to the Analysis of Algorithms", 2nd ed., Chap. 7.

Best regards,

jrgmendonca — Preceding unsigned comment added by Jrgmendonca (talk • contribs) 21:27, 4 November 2018 (UTC)

I certainly have no objection to having better references (and if not available in English, I don't object to them being in other languages). Please note that I did not revert your citation, I just moved it into the further reading section. My main concern was the issue of primary versus secondary sources. This is a major difference between writing a math paper, where primary sources are the standard, and writing an encyclopedia such as this, where we are reporting on what is in the secondary literature. --Bill Cherowitzo (talk) 05:22, 5 November 2018 (UTC)

Brocard's problem.

Hello. I saw the reversion you made on the content I added.

What should I do to get some attention to the global equality of a^b=c!+1 and a^b=c!-1?

I believe both are interesting and relevant in number theory.

Anyway I'm a student so I understand that my work is not professional and my poor formation.

But I had some ideas about different subjects that were "stolen" from me by others so they could put their names on it. So I tried to be more active this this time.

Anyway, sorry if I resulted bothering.

Álex Gómez 1813 (talk) 06:15, 5 November 2018 (UTC)

Hello Álex. My revert had nothing to do with the value of your contribution, only with Wikipedia policy regarding what is published. Wikipedia does not publish original work such as you have submitted, only material that has already appeared in reliable secondary sources. What you need to do is to get your ideas published elsewhere and then they can be referenced here. It is typical for a student to get some help in doing this from their professors, but it sounds like you have had some difficulty in doing this. If that is the case, try other professors, maybe even from different schools. --Bill Cherowitzo (talk) 18:59, 5 November 2018 (UTC)

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Wheat and chessboard problem

Why did you remove the link to "wheat" in this page? —Eli355 (talk • contribs) 17:36, 11 December 2018 (UTC)

As is pointed out in Wikipedia:SKYISBLUE it is not necessary to link to every word in an article. Good links help readers fill in the background to make the current article more understandable. Bad links are those that send a reader off on a wild goose chase trying to find a connection with the current article. In my opinion, this link to Wheat was a bad link since the problem (story?) has nothing to do with wheat. In fact, many versions use rice grains instead of wheat. The nature of the substances used on the chess board is really unrelated to the counting problem. --Bill Cherowitzo (talk) 18:38, 11 December 2018 (UTC)

Perhaps a better place to look at is MOS:OVERLINK, where my point is more clearly made.--Bill Cherowitzo (talk) 05:22, 12 December 2018 (UTC)

I understand, thanks for your explanation. —Eli355 (talk • contribs) 17:34, 14 December 2018 (UTC)

ISBNs

Please click the wiki markup on the ISBN changes I made. I think you will see they are all valid. Thanks. – S. Rich (talk) 05:40, 24 December 2018 (UTC)

Your changes removed the separators in the parts of the isbn numbers. I assume it was the bot you are using. This does not give an incorrect isbn, it just gives a poorer version of the isbn. With the separators I can read off the language, region of publication and publisher, but since these fields do not have the same lengths, this can not be determined without the separators. Some simply use the isbn as a single number identifier, but this is just needlessly throwing away information. I wish you would stop doing this. --Bill Cherowitzo (talk) 05:48, 24 December 2018 (UTC)

I doubt the average WP reader is so erudite as to distinguish language, region, publisher, etc from the ISBNs. Besides, this info is already part of the ordinary citation because the language is in the title page, the region is listed as "location=" or "place=", and the publisher is also cited. The average reader, if interested in a particular citation, will get the needed info when clicking the Book Sources link and then going to the WorldCat, Google, or Amazon links. Also please note that WorldCat, etc do not use hyphens in their presentations. My goal in these Vital Article edits is to produce a uniform/consistent presentation of the hyphens. If you don't like the changes you can revert the ISBN changes and I won't touch. But please don't use the roll-back function to change back the undisputedly helpful changes. Thanks. – S. Rich (talk) 05:59, 24 December 2018 (UTC)

Sorry for intrusion. Simply ignoring WP readers, erudite above some average level (so what!), and keeping a uniform/consistent presentation of the hyphens above their interests is impolite at best, if not even blatantly disruptive. Expecting those readers to save possibly undisputedly helpful parts in partly detrimental actions, covering many instantiations, is just ridiculous impertinence. Purgy (talk) 07:27, 24 December 2018 (UTC)

Thanks Purgy, a little harsher than I might have said it, but you certainly got the correct sentiment. And Srich32977, if you would actually read WP:ISBN you will find two statements about stylistic concerns. The first is, when given a choice, use ISBN-13 rather than ISBN-10. The second, and more to the point here, is that if dashes are present, they should be left in. This is then justified by the argument I gave above. As to my using roll-back, I examined all the edits you made on the two pages that I changed. In one case I manually corrected all the isbn's and left everything else alone. In the other case (Combinatorics), the other edits were pretty cosmetic and the work required to fix the isbn's was more difficult, so I rolled back. Let me make a counter-offer, if you don't change the isbn's, then I won't touch your edits.--Bill Cherowitzo (talk) 20:14, 24 December 2018 (UTC)

Thanks to both. In response I have not taken any 13 ISBNs and converted to 10s. The 13 is "my" preferred format too. Next, I noticed that the WP:ISBN talk page had a discussion 6 years ago about spaces & hyphens – I weighed this against the fact that all of the links from the referenced WP:Book sources to online text sources (i.e., WorldCat, Amazon, and Google) end up with un-hyphenated ISBNs. (I've seen the same result with the online database sources (such as Goodreads).) Well, What is an ISBN notes that "human readable" ISBNs can use hyphens or spaces. So there is a choice: consistent presentation of the machine readable ISBNs or an inconsistent mixed presentation of spaced, hyphenated, and unhyphenated/unspaced ISBNs. Since the overwhelming majority of WP readers are not hand-copying ISBNs I think a stylistically consistent presentation is better. – S. Rich (talk) 22:27, 24 December 2018 (UTC)

Two points to bring up. First of all talking about ISBN's as being machine readable is bogus. Machines do not read the numerical format, they read the bar codes, which, except for the large gap after the prefix, do not encode the dashes (but this is a characteristic of bar codes, not ISBNs). For my second point, ask yourself why, even after 2007, publishers still print both the ISBN-10 and the ISBN-13 numbers? ISBN-10 is not machine readable, never has been, so this is not a compatibility issue, but it is human readable, and if it didn't have some value then why bother continuing to print it? I think that you are trying to impose your personal preferences on the Wikipedia community without any consensus to do so.--Bill Cherowitzo (talk) 04:46, 27 December 2018 (UTC)

Grammar

"a corresponding element[without s]". Singular. Doesn't allow the correspondence to assign multiple elements. If you still have the hurge to introduce even more precision than that, add it, instead of reverting to a sentence that is indeed strictly defining the constant function only. Cactus0192837465 (talk) 04:03, 10 January 2019 (UTC)

"Pointwise application"

If you say that to get the number $\sin(42)$ the application of the function sinus to the number 42 is "pointwise," then how does the normal function application look like in your opinion? --Alexey Muranov (talk) 21:43, 16 January 2019 (UTC)

Here is an example of actual pointwise application: let $f$ be the function on real numbers that for each $x$ yields the operation of multiplication by $x$, and let $g$ be the identity function on the reals. Then the pointwise applictaion of $f$ to $g$ yields the function $h(x)=x^{2}$. --Alexey Muranov (talk) 21:51, 16 January 2019 (UTC)

Nice example. I think it would be good for the discussion to be in the talk page of Function composition. That error of calling it pointwise had been in that article for a long while. It is good if the explanation of why it is wrong is in a place easy to find for people editing that article. Cactus0192837465 (talk) 22:18, 16 January 2019 (UTC)

Also, one should not say "poinwise sum of the result of $f$ and the result of $g$" when what one means is the poinwise sum of $f$ and $g$. --Alexey Muranov (talk) 08:14, 17 January 2019 (UTC)

Mea culpa. I apologize for that revert. I guess that I should not do any editing while suffering from a head cold. --Bill Cherowitzo (talk) 20:36, 17 January 2019 (UTC)

Regarding Four-dimensional space#cross-section

I have tried on several occasions to correct an error in this section. My corrections have been undone each time. If an observer in a two dimensional world observed a spherical balloon pass through, the observer would not, as the error suggests, see a point, then a circle getting larger, then getting smaller until it became a point just before disappearing. A circle on a plane can only be observed from a position above or below the plane. An observer within the plane would at best see a line segment. The observer would be able to infer the circle by making observations of the line segment through changes in position along the x,y axis to discover an arc length, but the observer would be unable to see the circle. Robin Les (talk) 22:39, 8 February 2019 (UTC)

Hi Robin. Technically you are right and this point is brought up in Abbott's Flatland in section 5. Everything looks like a line segment or union of line segments and points, so it is necessary for Abbott to describe ways that different shapes can be distinguished from each other. Consider the 3D analogy. If we look at a balloon (idealized) we do not see a sphere, we only see a disk. Lighting and other clues help our minds interpret this and see a sphere. It is in this sense that an observer in Flatland can see a circle. --Bill Cherowitzo (talk) 04:46, 9 February 2019 (UTC)

March 2019

Hello, and welcome to Wikipedia. You appear to be repeatedly reverting or undoing other editors' contributions at Euclidean geometry. Although this may seem necessary to protect your preferred version of a page, on Wikipedia this is known as "edit warring" and is usually seen as obstructing the normal editing process, as it often creates animosity between editors. Instead of reverting, please discuss the situation with the editor(s) involved and try to reach a consensus on the talk page.

If editors continue to revert to their preferred version they are likely to be blocked from editing Wikipedia. This isn't done to punish an editor, but to prevent the disruption caused by edit warring. In particular, editors should be aware of the three-revert rule, which says that an editor must not perform more than three reverts on a single page within a 24-hour period. Edit warring on Wikipedia is not acceptable in any amount, and violating the three-revert rule is very likely to lead to a block. Thank you. Dr. K. 04:09, 2 March 2019 (UTC)

You've got to be kidding! All I did was to revert your rather poor edit.--Bill Cherowitzo (talk) 18:50, 2 March 2019 (UTC)

Search problem

Hi! I saw that you discussed on Talk:Search problem#Needs improvement. You may be interested in discussing my suggestion to delete this article, after integrating its valuable parts (if any) where they fit. Best regards - Jochen Burghardt (talk) 12:53, 14 March 2019 (UTC)

Question Re Recent Edit That Was Reverted

Hello.

Recently (March 13) I added an external link to the article titled "Factorization". Shortly after that you reverted the edit, and explained:

  Reverted good faith edits by Evan2184 (talk): As per WP:ELNO #1 
  

I wish to apologize for violating Wikipedia policies. There was no ill intent and I appreciate that you referred to the edit as "good faith". I am quite new to editing on Wikipedia and I have been learning through trial and error, and through the helpful advice of other editors.

In addition to reading Wikipedia documentation, I have tried to better understand policies and guidelines by reading as many other articles as possible.

I added the edit to the External Links section of the article titled "Factorization" because I felt the page the edit linked to elaborated on the topic and contained examples and explanations that helped the reader gain a better understanding. I have seen other math articles where the External Links section contained links to pages that were elaborations of the article's topic. For instance, the article "Completing the Square" contains this link:

https://study.com/academy/lesson/how-to-complete-the-square.html

Also, the article "Ruffini's Rule" contains this link:

https://www.purplemath.com/modules/synthdiv.htm

In your revert you cited reason #1 of WP:ELNO. I would agree that the link in my edit is not a unique resource. But I'm not sure the other two links could be classified as unique resources either.

So, perhaps it's a bit of a gray area and a judgment call.

I would be grateful if you would reconsider accepting my edit. But mainly I want to improve my understanding of best practices and hope you can offer some guidance.

Thank you very much!

Evan Evan2184 (talk) 01:37, 20 March 2019 (UTC)

Hi Evan, I don't think that there is a gray area here. WP:ELNO #1 is pretty clear:

generally avoid providing external links to: 1. Any site that does not provide a unique resource beyond what the article would contain if it became a featured article. In other words, the site should not merely repeat information that is already or should be in the article.

One reason that this is important is that we do not want Wikipedia to devolve into a link farm as so many sites on the web have. We are building an encyclopedia, not a directory to what is available on the web. If information is important enough to be in the article, then it should be put in the article unless there are good reasons to avoid doing that (the reason for using the term generally above is to deal with such exceptions). The fact that there are links in other articles that seem to violate this is not a reason to expand the number of violations. Good links will survive and bad links will disappear, eventually ... it takes some time before editors get around to weeding out the links that shouldn't be there. --Bill Cherowitzo (talk) 22:34, 20 March 2019 (UTC)

Dear Bill, Thank you for your reply. It was very helpful.

I noticed that the page my edit linked to contains what seem to be a very large, perhaps randomized, number of examples, with quite good explanations of the steps involved in finding the factors of an integer. By clicking the button "See Examples" you can see examples and step through the explanations.

In a sense this might be considered a unique resource because even if the Factorization article were expanded to a featured article it would not contain an abundance of examples and the ability to step through the explanations.

I work tutoring math at an academic support center and my experience is that students often gain a better understanding of math concepts through a variety of examples and detailed, worked-out solutions. I feel the link would enhance students' understanding, and would not merely repeat information in the article.

Thank you!

Evan2184 (talk) 02:08, 21 March 2019 (UTC)

I totally agree that students need a variety of examples and worked-out solutions. However, this raises another issue, and that is Wikipedia:NOTTEXTBOOK. Encyclopedia writing and textbook writing are very different undertakings. This link would be more appropriate in a sister project such as Wikiversity that is structured more like a textbook. --Bill Cherowitzo (talk) 19:54, 21 March 2019 (UTC)

Search problem

Hi! I saw that you contributed (in 2016) to the article search problem; so you might be interested in the discussion at Talk:search problem#Undone deletion. Best regards - Jochen Burghardt (talk) 20:31, 9 June 2019 (UTC)

U+2212

−

Hello.
This thing is called the minus sign. It is a mathematical symbol, not a general-typography device. When you replace “-” with it in math formulae, you make a good job. When you insert it (or other characters from the Mathematical Operators block) to a running English text, you promote ignorance and stupidity on par with numerous “fixes” by IPs and red-faced accounts which are usually—on this site—bluntly reverted. Just avoid touching any typography in a running text if you are “too busy” to look at respective manuals. Incnis Mrsi (talk) 14:52, 19 July 2019 (UTC)

Woohooo

Hey, Wcherowi. I'd like to wish you a wonderful First Edit Day on behalf of the Wikipedia Birthday Committee! Have a great day! Mjs1991 (talk) 05:47, 10 August 2019 (UTC)

Thank you. It has been an enjoyable eight years. --Bill Cherowitzo (talk) 17:17, 10 August 2019 (UTC)

Divison by zero

Hi@Wcherowi ,You recently reverted my edit in the page https://en.wikipedia.org/wiki/Division_by_zero ;where in the elementary arithmetic section I had replaced 'cookies' with 'apples'. You reverted saying that my edit was meaningless. But the word 'apples' has 1 character less than the word 'cookies';so by 11 replacements we get 11 characters less in a encyclopedia bearing same meaning. What do you say? A Seeker of Truth (talk) 04:09, 9 September 2019 (UTC)--A Seeker of Truth (talk) 04:09, 9 September 2019 (UTC)

I say that is meaningless.--Bill Cherowitzo (talk) 17:02, 9 September 2019 (UTC)

Recent edits

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. --Rupert Loup (talk) 00:44, 9 November 2019 (UTC)

I think that I owe you an apology. I'm sorry for taking your comment in a wrong way, I let myself get carried away. Rupert Loup (talk) 19:53, 10 November 2019 (UTC)

Ok. All is forgiven. --Bill Cherowitzo (talk) 19:55, 10 November 2019 (UTC)

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Reverting edit on Euler number page

The formulas which have been deleted came from refereed Math journal. I was thinking of including more information, but you deleted the information I added due COI. The page contains little information compared to what is there in literature. Only researchers in this area can contribute to such pages. Please check for the references in such cases, like the one which is not working on that page, and comes from a non-referred source.

On Wikipedia we place new entries at the bottom of the page (unlike other places on the web) so I took the liberty of moving yours here, I hope you don't mind.

In response let me say that I thought my edit summary was clear, but I can amplify it here. First of all, WP takes a dim view of editors putting up their own papers as references. This conflict of interest is taken very seriously and needs to be avoided to maintain the integrity of the encyclopedia. Your impartiality is put into question when you placed your new formulas ahead of the traditional well-known examples. Just being published in a refereed journal is not sufficient to determine notability of an addition. Time is needed for the paper to be reviewed and vetted by the mathematical community and the 2019 publication dates make it clear that not enough time has elapsed. If you have the expertise that you claim, you would be more useful to the encyclopedia if you could improve the references used on this page rather than push your own work.--Bill Cherowitzo (talk) 23:20, 22 November 2019 (UTC)

Bill, I am inclined to agree with you here, but haven't had the time to look closely at the edits to see how much was worth saving. I also noticed that today, another brand-new account added a similar section (with the same reference) to alternating permutation; see [1]. --JBL (talk) 20:20, 26 November 2019 (UTC)

Thanks Joel. Yes I also spotted that yesterday and suspect that we have a case of sock-puppetry here. I didn't follow up on the original post since he came back with some good edits in the article (but did not take down his own paper) and no other editors backed me up. I am a bit torn about this as the editor seems to have good contributions to make, but does not appear to be willing to abide by our norms. --Bill Cherowitzo (talk) 20:15, 27 November 2019 (UTC)

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Peace is a state of balance and understanding in yourself and between others, where respect is gained by the acceptance of differences, tolerance persists, conflicts are resolved through dialog, peoples rights are respected and their voices are heard, and everyone is at their highest point of serenity without social tension. Happy Holidays to you and yours. ―Buster7 ☎ 13:57, 24 December 2019 (UTC)

Regarding your revert of edit about number of smallest asymmetric cubic graphs

I very rarely edit Wikipedia, so I am not deeply familiar with the procedures. The statements I changed were added in 2011 with no citation: https://en.wikipedia.org/wiki/Special:Contributions/71.201.65.77 They're wrong, see https://math.stackexchange.com/q/3540720/ I do not think it is possible to find any citation for there being 5 such graphs and not 2, but this fact is fairly trivial to verify with modern graph theory software. For example, with Mathematica and gtools/nauty: Select[Import["!geng -d3 -D3 12", "Graph6"], GraphAutomorphismGroup[#] === PermutationGroup[{}] &] (and also try for smaller vertex counts than 12 to see that there are none). My intention was to correct a mistake. Can you help me do this while ensuring that procedures are followed? BarroColorado (talk) 08:04, 12 February 2020 (UTC)

As is typical on Wikipedia talk pages, new messages go on the bottom of the page (unlike many places on the web), so I took the liberty of moving yours here. I do apologize for reverting your changes, you were in fact correct. But, in my own defense, the edit summary you provided indicated that this was your own work using appropriate graph theory software. This is considered WP:OR since the computations are not trivial ones that can be verified by the majority of our readers. What is needed here is a citation by a reliable source and this was provided by another editor who reverted all my changes. I am glad that this was finally corrected in a way that is acceptable under Wikipedia policies. --Bill Cherowitzo (talk) 18:46, 12 February 2020 (UTC)

There is no need for an apology. Thanks for keeping Wikipedia reliable! I could not find a reference myself, I could only verify it with software. In fact, I found the mistake while testing graph theory software. I'm glad that someone found a reference. BarroColorado (talk) 12:41, 13 February 2020 (UTC)

Lewis Carroll

Please explain why you are any more qualified than I am to judge the reliability of a biographical source on Lewis Carroll. One only needs to use their eyes to see that the photos in question are fake, anyway. — Preceding unsigned comment added by DarwinGalileiHerschelHuygens (talk • contribs) 21:38, 17 February 2020 (UTC)

This has nothing to do with qualifications, it has to do with Wikipedia's policies: you can read about them here. I have started a discussion on the article talk page in the hope that you will explain what you're doing and why. --JBL (talk) 22:03, 17 February 2020 (UTC)

Mulitiplication of vectors Reverting unexplained content removal Comment

Re: your revision https://en.wikipedia.org/w/index.php?title=Multiplication_of_vectors&oldid=935778784

Can you please explain:

• How the product in an Algebra over field doesn't constitute a bilinear product?
  
• Why if your concern is discussion of bilinear products, you chose to revert to a version that still discusses bilinear products?

--Eassin (talk) 18:10, 20 February 2020 (UTC)

The dot product, yes, and the statement was already there. But you included this statement under cross product which I considered a muddying of the waters.--Bill Cherowitzo (talk) 21:21, 20 February 2020 (UTC)

Length

I was going to try to improve this article. It is this week's article for improvement. You persuaded me not to bother.
Since this is in your bailiwick, maybe you could improve it. You know better, so have at it. 7&6=thirteen (☎) 20:27, 23 February 2020 (UTC)

Editing Condorcet's Jury Theorem

Hello,

I am a first-time contributor to Wiki and am unsure of proper protocol. I replaced the previous version of the "alternative proof" section in Condorcet's Jury Theorem here (which had no discernible proof) to an inductive proof that is my own work. You flagged the section as having to citations, and I am unsure how to proceed, or whether the proof currently on the page belongs there at all.

Apologies for editing your personal talk page - again, I am new at this. Any help would be appreciated.

Thanks!

Hi. One of the mainstays of Wikipedia is that we do not include our own work in the articles (WP:NOR). This can be very frustrating when we see a glaring gap in an article that we know how to fill, but someone (like me) comes along and declares that it needs a citation. Wikipedia reports on what is available in the literature, not on what its editors can devise. Most editors would have removed the section, but I had hoped that you were familiar enough with the literature to find a version of this induction proof that could be cited. Failing that, it ought to be removed. The advice that is most often given is that if you want to see your own work on Wikipedia, you need to first get it published and vetted by the mathematical community ... and even then there are conflict of interest (WP:COI) issues. I hope you aren't too discouraged by this.--Bill Cherowitzo (talk) 01:16, 2 March 2020 (UTC)

No problem - I reverted the page to the previous version, keeping the flags you added on the sections without references. If I find a published version of the induction proof, I will insert it later. Sorry to muck things up... I will refrain in the future. Thanks for your help! — Preceding unsigned comment added by 2601:644:100:66A0:68C8:6CFD:BE1B:F721 (talk) 02:08, 2 March 2020 (UTC)

WP:ELNO details

Hi, Wcherowi! I have noticed your revert of an external link at Median (geometry). Could you be more specific re the mentioned external link and the 19 situations mentioned at WP:ELNO, which one do you consider that it applies to the external link? (Thanks!)--109.166.130.189 (talk) 22:19, 20 March 2020 (UTC)

From that page: No page should be linked from a Wikipedia article unless its inclusion is justifiable according to this guideline and common sense. The burden of providing this justification is on the person who wants to include an external link. But also the answer to your question is 1 and some nonempty subset of {10, 11, 12}. --JBL (talk) 23:59, 20 March 2020 (UTC)

Revisiting both WP:ELNO and the mentioned link Algebra.com, I think that is not quite clear why 1 and a combination of 10, 11, 12 would apply. Are the links including Lessons...and especially Answers Archive not suitable? I also think that the link contains a valuable content re the proof of the statement The medians of a triangle are concurrent, which I see that is not present in the article. I presume that instead of just being include as a link, it could be cited for the proof content re concurrent medians.--109.166.130.189 (talk) 00:51, 21 March 2020 (UTC)

I was revisiting some elementary geometry proofs re triangles (that passed somehow unnoticed some 28 years ago) and looking for the actual proofs when encountered the mentioned link which I think is very good re the proof content.--109.166.130.189 (talk) 00:59, 21 March 2020 (UTC)

Subjunctive mood

Hi again! Re the reversion at Angle bisector theorem described as improper English, what exactly is improper in using the subjunctive mood of the verb to be instead of the imperative construction with let? (Perhaps another description would be more accurate, and perhaps the reversion be annuled!)--109.166.130.189 (talk) 23:42, 20 March 2020 (UTC)

Per MOS:MATH#TONE, sentences should not begin with symbols, so there is no chance that your first version will be reinstated. --JBL (talk) 00:03, 21 March 2020 (UTC)

Interesting situation! The ref to MOS:MATH is a much better description than improper English. But is the use of let making much difference to be in accordance with MOS:MATH?--109.166.130.189 (talk) 00:29, 21 March 2020 (UTC)

I totally agree with JBL and thank him for his intervention here. I admit to being a bit sloppy with my edit summary, it should have read "improper English in a mathematical context". We do not use the subjunctive mood when writing mathematics (it's a matter of clarity) and when I see it I am jarred. The imperative construction with "let" is, by far, the standard in mathematical literature and my reaction was just a reflection of that. --Bill Cherowitzo (talk) 19:30, 21 March 2020 (UTC)

Snakes and ladders

I noticed you removed an entry in Snakes and ladders. What do you mean "unsupported trivia"? 172.250.44.165 (talk) 20:15, 6 April 2020 (UTC)

Unsupported means that you provided no reliable source for this claim, that is, no secondary source that describes this use of "Snakes and Ladders". Trivia means that the addition had no redeeming value with respect to the topic. A simple mention of the name does not add anything to the article. If, however, the game (either playing it or using its rules) was an integral part of advancing the plot, then its inclusion would not be trivia. --Bill Cherowitzo (talk) 20:33, 6 April 2020 (UTC)

ISBN

The two statements are not equivalent. While it is true that only 10 digit numbers were issued before 1 January, 2007, after 1 January, 2007, both 10 and 13 digit numbers were issued - quite a few books even contain both a 10 and a 13 digit ISBN. It is fairly straightforward to convert between 10 and 13 digit numbers - they are basically the same number, with different check digits appended plus the 13 digit version has the "bookland" prefix prepended to make it compatible with the EAN code. — Preceding unsigned comment added by Jost Riedel (talk • contribs) 16:59, 19 March 2020 (UTC)

On Wikipedia talk pages we generally put new comments at the end of the page (unlike other places on the web), so I have taken the liberty to move your comment here. I hope you don't mind.

What you say is basically correct, but after Jan 1, 2007 book publishers were required to use ISBN-13. Many continue to use both, in part because ISBN-10 has a superior error detecting capability (it can detect more kinds of errors). While compatiblity with EAN code was a desireable property that went into deciding on the form of the prefix, the real reason the switch was made had to do with the fact that the industry could see that they would be running out of ISBN-10 numbers and needed a way to expand the range without destroying the current numbers. When the original ISBN-10 numbers run out (they haven't yet), all that is needed is a change in the prefix to provide a new range of numbers. When that occurs it will no longer be possible to use ISBN-10 numbers as they will no longer be unique.--Bill Cherowitzo (talk) 20:28, 19 March 2020 (UTC)

A book published before Jan 1, 2007 does of course have a 10 digit ISBN - except if it reprinted after that date, then it may have a 13 digit ISBN as well. One example: Alan Burns and Andy Wellings: Real-Time Systems and Programming Languages. Addison-Wesley, 2001. It has ISBN 0-201-72988-1 printed inside (it is an unchanged printing, after all), but sports a 13 digit ISBN with matching barcode on the back cover. I do think the main reason for 13 digit numbers was EAN compatibility. After all, besides the currently used bookland (978) only one other country code (979) is reserved for ISBN, and 979-0 is excluded (for International Standard Music Numbers (ISMNs)). So there less than double the amount you can address with 10 digit numbers - hardly worth the effort.--Jost Riedel (talk) 16:25, 30 March 2020 (UTC)

Not sure where you are getting your information from. Take a look at History of the ISBN system. ISBN-13 is now required, with ISBN-10 optional. I have lots of books with both ... I don't know what your example is supposed to prove. The prefix (978 currently and 979 in the future) is not a country code. The country/language code is the next set of numbers and it has variable length. ISMNs are not ISBNs, so 979-0 is not prohibited from use in ISBN-13s. The new prefix gives an exact doubling of the number of numbers available. Expansion beyond the 979 prefix is certainly possible, but talks are currently underway to revise the entire system, so there may be an entirely new system way before that limit is hit.--Bill Cherowitzo (talk) 21:59, 31 March 2020 (UTC)

Take a look at [2] - "System Code. This is the leftmost 2 or 3 digits and generally identifies the country of the manufacturer. ... In the case of the ISBN, the system code of either 978 or 979 is used to signify a fictitious land where books come from, namely Bookland.". With "normal" EANs, the first 2 or 3 digits are used for a country code, to accomodate ISBNs within this numbering scheme only system codes that are not used elsewhere can be used. And ISBN retain their own country code.Jost Riedel (talk) 22:32, 3 April 2020 (UTC)

I see nothing in that page that counters anything that I have said. The main point, why the switch to ISBN-13, is addressed a little deeper in that web site at The 13 digit ISBN. The change made the system compatible with EANs, not identical to them. In particular, an ISBN-13 has 5 fields while an EAN-13 has only 4 fields. Once one of these structured numbers is formed, the fields can be ignored which is what gives the compatibility (together with the error checking algorithm). That means, if you look at an ISBN-13 as EAN code, the first 3 digits will be interpreted as a country code (bookland) as you have mentioned, but if you don't view it that way, then the prefix is just one of two possible values and does not indicate a country code (which is what I tried to say above). If you take an ISBN-13 number and try to read off the EAN fields, you get garbage (and vice versa). As I said, the systems are compatible, not identical. --Bill Cherowitzo (talk) 19:25, 7 April 2020 (UTC)

Mathematics notation added to the Least common multiple article

Hi, can you explain to me or point me to the direction that I can understand this (as I'm a newcomer), I added these math tags in the article based on another feature article that I saw before with the logic that these tags make variables (and other things) more readable – Erfan Talk☻ 16:24, 14 April 2020 (UTC)

(talk page stalker) @Et0z1: I think this is answered by the first few paragraphs of MOS:FORMULA. (Is the current situation frustrating? Yes. But also any plausible alternative would also be frustrating, just in different ways.) --JBL (talk) 18:19, 14 April 2020 (UTC)

Joel has pointed you to the right page that discusses this. Let me just add a few comments of my own. There is no universally agreed upon way to write mathematics in WP articles (the frustration that Joel mentioned), so it is up to individual editors to make judgments about appearance and readability. In my opinion, in-line TeX degrades the appearance rather than improve it. On the other hand, the sans serif font used by WP (although preferred by some math editors) jars my mathematical sensitivity. To this end, in my own edits, I prefer to use {{math}} (html with a serif font) in-line and <math> to display math on its own line. I do not convert articles to my style unless they are written in a hodge-podge of styles and there is a need to do something about the appearance. The overriding concern is the appearance of the page and unless there is a need to do so, wholesale changing of the style is frowned upon. --Bill Cherowitzo (talk) 19:31, 14 April 2020 (UTC)

Thanks both of you, I haven't read the MoS and it explicitly states my mistake sorry. thanks for your explinations – Erfan Talk☻ 09:26, 15 April 2020 (UTC)

Perimeter

The paragraph about the perimeter of general shapes in Perimeter is flawed.

In some cases the integrand is a Transcendental function, so can't be replaced with an algebraic formula. Sometimes the integral of transcendental function is algebraic, but even then there is no guarantee that the equation will have an algebraic solution, making determining L impracticable.

At the moment it's like saying a quintic equation must be solved to determine L, with no mention that is rarely possible. After thinking a moment, it will be sufficient to say "must be replaceable with by" instead of "must be replaced with by"

Also, ellipses are a common shape with a perimeter that's impracticable to determine, since they require Elliptic integrals. Using them as an example could be useful. The Ellipse section gives a formula for the perimeter using elliptic integrals, so should probably also be linked to.

Carandol (talk) 22:05, 5 May 2020 (UTC)

I don't disagree with what you have said above, except in calling it a "flaw". There are just some things in mathematics that do not have closed form expressions. We have learned to live with this. The whole field of numerical approximation is driven by this difficulty. Perhaps a little more can be said in the article about the possible intractability of the problem, but this doesn't seem to be the right place to elaborate on that.--Bill Cherowitzo (talk) 20:20, 6 May 2020 (UTC)

Where would be the right place then? This seems as good as any, unless there's a page somewhere, listing problems like that. 'We have learned to live with this' but can we expect the reader to? Are they likely to even be aware there is a problem? Carandol (talk) 20:39, 6 May 2020 (UTC)

I'd suggest that a link to arc length#Finding arc lengths by integrating would suffice

Agreed. I'd put the link on 'the length of the path', the length of the path

By the way, this discussion should really be on the Perimeter talk page, since other editors may be interested in contributing. If you want to continue this, I'll move this discussion there. --Bill Cherowitzo (talk) 20:51, 6 May 2020 (UTC)

Fine by me. That'll more than cover all the concerns I originally had. I think I originally considered that option, but ruled out for reasons I've now sure don't hold water.

The main reason I didn't use the Perimeter talk page was that it was last used in 2015 so a new edit probably wouldn't be noticed. Obviously, this exchange demonstrates that I was wrong.

Coset

Thanks for reviewing my attempt to improve Coset. Perhaps, because I am not a mathematician, I was unsure of the notation used in the article to define a coset, and confused about the exact number of cosets of a subgroup.

The definition includes the phrase, "given an element g of a group G." Because G has eight elements, I expected there would be eight values of g, and therefore eight left cosets and eight right cosets. However, in the illustration the article said, "There are four left cosets of H," leaving me confused about exactly what was meant by "coset". Is there one coset for each element of G, or is a coset a coset only if it is different from the other cosets?

I think the illustration actually shows the quotient group G/H, rather than all the left cosets of H in G.

Please excuse my poor word choice. I did my best to make the article more understandable by non-experts. I hope you will consider making a more skillful improvement than I was able to do.

I will watch this spot in case you decide to comment.

Thanks for all your valuable contributions to Wikipedia. Comfr (talk) 16:40, 16 May 2020 (UTC)

This discussion really belongs on the article's talk page, but I'll give a brief response here. You are correct in pointing out that the article's introduction leaves much to be desired. I could see what you were trying to express, but it came out more confusing than not. Each element is in a unique (there is only one) coset, but the cosets are not distinct (different from one another). The rule for telling when two cosets are equal is given in the third paragraph, but it would take some familiarity with the subject to glean the consequences of that rule. Perhaps a better way to see what is going on is to say that the distinct cosets form a partition of G (every element of G is in exactly one piece [coset] of the partition). The illustration shows this partition by listing all of the distinct cosets of G. The illustration can also be interpreted as the underlying set of the quotient group G/H (its not a group until you specify how the cosets are to be added). I've been thinking of how to rewrite the lead of the article and have been toying with the idea of introducing the partition idea early on. Does this make sense to you? --Bill Cherowitzo (talk) 00:06, 17 May 2020 (UTC)

Thanks for your detail response. Comfr (talk) 16:44, 17 May 2020 (UTC)