Wikipedia talk:WikiProject Mathematics/Archive/2021/Feb

math display=block

MOS:MATH says that <math display=block> must be used instead of a colon for displaying a formula. Having testing this, it appears that this provides a bad result: the vertical space before and after the formula is much larger than with a colon. This is definitely confusing as suggesting that the formula is a paragraph by itself, even when the formula is in the middle of a sentence. So, I think that this recommendation must be removed until this bug will be fixed. (I do not know how to submit a bug report for such a case, and submitting a bug report would be more efficient if supported by a consensus.)

By the way, if one want that editors use <math display=block>, this must be added to "Math and logic" menu. D.Lazard (talk) 11:47, 2 February 2021 (UTC)

I agree the spaces give a wrong impression (and also look ugly). Jakob.scholbach (talk) 12:19, 2 February 2021 (UTC)

Can you give an example where you think it looks bad? I have used it in various articles, and have never noticed such an issue. —JBL (talk) 12:46, 2 February 2021 (UTC)

I wonder if there is some confusion here in which someone is mistaking <math display=block> for <blockquote>. I would agree that the latter puts too much space above and below the displayed line. Michael Hardy (talk) 02:18, 4 February 2021 (UTC)

I wonder if someone is comparing <math display=block> to colon-math with blank lines above and below the math, and not noticing that with <math display=block> it makes a difference whether there is a paragraph break before or after the display. If you want to use <math display=block> within a paragraph of text, and make it look like it is a displayed math block within that paragraph, you need to not format it as its own separate paragraph. —David Eppstein (talk) 04:24, 4 February 2021 (UTC)

Trying out all the options. A blank line before a colon-math

$E=mc^{2}$

Using a blank line after colon-math

$E=mc^{2}$

Using blank line before and after colon-math

$E=mc^{2}$

Using blank line before display=block

$$E=mc^{2}$$

Using blank line after display=block

$$E=mc^{2}$$

Using blank line before and after display=block

$$E=mc^{2}$$

On my machine, google chrome on a Chromebook, and MathML with SVG or PNG fallback, I can see no difference in the indentation of any of these. There might be a bug here but we would need to see a reproducible example. p.s. When quoting code examples its good to wrap them in <nowiki>...</nowiki> tags to prevent the parser from trying to interpret the tag. The {{tag}} template is handy for this as well. --Salix alba (talk): 06:55, 4 February 2021 (UTC)

• It's not the indentation but the vertical spacing around them. And I don't think it's actually a bug, but more a level of control that's not available with the colons. For me, Chrome on OS X, the blank lines are visible as extra space in the math display block versions, but not the colon math versions. Did you also notice that if you place
  $${\text{an equation}}$$
  in the middle of an bulleted item list, it is properly double-indented, and your bulleted paragraph continues with the correct indentation afterwards? —David Eppstein (talk) 07:06, 4 February 2021 (UTC)

Here is an example taken from the lead of Change of basis that I have recently edited, firstly with a colon,

$\mathbf {x} _{\mathrm {old} }=\mathbf {A} \,\mathbf {x} _{\mathrm {new} },$

followed with the same with "display = block"

$$\mathbf {x} _{\mathrm {old} }=\mathbf {A} \,\mathbf {x} _{\mathrm {new} },$$

In both case, there are no blank lines in the source before or after the displayed formula. As the formula is inside a sentence, the extra vertical space before the formula with "display=block" is definitively a bug. Surprisingly, there is no visible extra vertical space after the formula, although there was one when I edited the article (smaller than the extra space before the formula). Possibly, the implementation of "display=block" has been modified since the opening of this thread. D.Lazard (talk) 08:25, 4 February 2021 (UTC)

It looks like the spacing in the second example is controlled by the style sheets in MediaWiki:Common.css. In particular

/* Make <math display="block"> be left aligned with one space indent for 
 * compatibility with style conventions
 */
.mwe-math-fallback-image-display,
.mwe-math-mathml-display {
	margin-left: 1.6em !important;
	margin-top: 0.6em;
	margin-bottom: 0.6em;
}

Reducing the amount of space with margin-top: 0.4em; should give similar spacing. We can do this locally, anyone with the appropriate admin bit can do it. It would be better if people add this to their Special:MyPage/common.css so we can properly test in first before making it live.

It highly unlikely the implementation has changed, as it takes months to get the smallest change through code review. This bit of the CSS was added by me in 2015[1] and has not been changed since. --Salix alba (talk): 13:15, 4 February 2021 (UTC)

As a guess, the CSS is targeting the child elements of the actual sibling element, which is <div class="mwe-math-element">. This margin is probably not being collapsed, hence, irregular spacing relative to what would be available with <p>. (Regardless, I do not really understand why we're targeting the two classes rather than the parent.) --Izno (talk) 00:56, 5 February 2021 (UTC)

Wikipedia:Sandbox organiser

Sandbox Organiser A place to help you organise your work

Hi all

I've been working on a tool for the past few months that you may find useful. Wikipedia:Sandbox organiser is a set of tools to help you better organise your draft articles and other pages in your userspace. It also includes areas to keep your to do lists, bookmarks, list of tools. You can customise your sandbox organiser to add new features and sections. Once created you can access it simply by clicking the sandbox link at the top of the page. You can create and then customise your own sandbox organiser just by clicking the button on the page. All ideas for improvements and other versions would be really appreciated.

Huge thanks to PrimeHunter and NavinoEvans for their work on the technical parts, without them it wouldn't have happened.

Hope its helpful

John Cummings (talk) 11:31, 6 February 2021 (UTC)

Requested move 20 January 2021

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Moved. Generalized version moved to Generalized Stokes' theorem to be consistent. (non-admin closure) Vpab15 (talk) 22:54, 12 February 2021 (UTC)

---

• Kelvin–Stokes theorem → Stokes' theorem
• Stokes' theorem → Generalized Stokes theorem

– WP:COMMONNAME says that names used most frequently in reliable sources should be used on Wikipedia 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" $\mathbb {R} ^{3}$ 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 $\mathbb {R} ^{3}$. "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 $\mathbb {R} ^{3}$ is far more common for a non-specialized audience. — MarkH₂₁^talk 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 $\mathbb {R} ^{3}$, 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)
    • The alternative proposal below looks like a better way to achieve what I was attempting. Certes (talk) 13:03, 2 February 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 Wikipedia 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 $\mathbb {R} ^{3}$. 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 Wikipedia 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)

    An interesting read, thanks; this paper should be cited. Now, even Katz doesn't seem to suggest the theorem should be called Kelvin-Stokes' theorem, so we're left with the two references in Japanese - for those who can read - which, I'm afraid, isn't enough to claim most common use in English (WP:NCUE). Some credit should be given to Hankel, Kelvin & Tait in the article, per Katz's paper, but it's not on us, I think we all agree, to push this or that alternative name. Ponor (talk) 15:25, 25 January 2021 (UTC)

Alternative proposal

I'd like to see Stokes' theorem become a new broad concept article briefly covering both the original theorem and its generalisation.

To do this we would disambiguate the current article (but I'm not convinced that the proposed name Generalized Stokes theorem is particularly recognisable) and start a new BCA. The existing articles are both OK in what they cover.

I think this new article could be a very valuable one, particularly if it is kept short and approachable to the uninitiated. Andrewa (talk) 09:30, 2 February 2021 (UTC)

• After looking up broad-concept articles, I appreciate this proposal. However, I'm a physicist and not a mathematician, so I don't understand the general case enough to tell whether a BCA would be appropriate. I will leave that decision to the mathematicians of Wikipedia. ChromaNebula (talk) 23:50, 6 February 2021 (UTC)

---

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

About Oka's lemma

I think it's okay to merged it into Kiyoshi Oka. Oka's coherence theorem may also be included.--SilverMatsu (talk) 05:00, 12 February 2021 (UTC)

I wouldn't merge them. In both cases, I trust R.e.b.'s judgement about which topics should have separate articles, even if those articles were left in a very stubby state. —David Eppstein (talk) 05:15, 12 February 2021 (UTC)

I would agree that Oka's coherence theorem is important enough as a foundation result in its field (complex geometry and algebraic geometry) to warrant its own page, even if it is currently a stub. Kiyoshi Oka is a reasonably significant figure also, as one of the big early Japanese geometers, so should also obviously warrant their own page, so I would say don't merge those two. I can't speak with any confidence about Oka's lemma.Tazerenix (talk) 05:34, 12 February 2021 (UTC)

Thank you for your reply. I agree that Oka's coherence theorem is a separate page. However, it seems that Oka's lemma may be written on the pseudoconvex domain or the Levi's problem page. Currently, Levi problem is redirected to the Stein manifold, which seems more like Grauert's proof than Oka's proof. thanks!--SilverMatsu (talk) 06:05, 12 February 2021 (UTC)

I found three more sources in MathSciNet with "Oka's lemma" in the title (all about this specific lemma; there's another paper on a different Oka lemma). I think it clearly passes WP:GNG as an independently notable topic. —David Eppstein (talk) 06:34, 12 February 2021 (UTC)

Thank you for your reply. As for Oka's coherence theorem, it would be nice if I could prove it, but I think I'll probably have to wait 70 years from 1978. The content of the current Oka's lemma is a bit questionable, given that Levi pseudoconvex and Levi's problems are redirects. The current content semms like a pseudoconvex domain. In some cases, the content of Oka's lemma is defined as pseudoconvex. but, called Oka Pseudoconvex has a different meaning ...--SilverMatsu (talk) 07:30, 12 February 2021 (UTC)

Apparently, there are two more theorems called Oka's coherence theorem. To mention this, we need the following Oka's and Cartan paper. As for the ideal sheaf, Cartan also submits proofs independently, so it seems that this theorem cannot be merged on Kiyoshi Oka page. Special thanks to David Eppstein and Tazerenix for their advice. I would like to hear your opinion on adding these two coherence theorems to the page. thanks!--SilverMatsu (talk) 12:03, 13 February 2021 (UTC)

Combinatorial hierarchy

This looks like bad numerology, and it's entirely relying on primary sources because everyone apart from these few authors realizes it's not useful. Is there a good reason to keep this article? --mfb (talk) 22:23, 11 February 2021 (UTC)

Looks like 100% crankery to me. If it's notable enough for people to have written about the fact that it's crankery, then obviously such sources should be included; if not, AfD seems like a good option to me. --JBL (talk) 22:44, 11 February 2021 (UTC)

I'm not finding anything except a passing mention in an essay by I. J. Good about how, yes, you can screw around with numbers and get other numbers that look meaningful. I don't think that warrants an article. The biographies linked from combinatorial hierarchy also need attention. XOR'easter (talk) 14:00, 12 February 2021 (UTC)

All the work of H. Pierre Noyes uses "personal interview" as reference, great. That's arguably worse than Noyes writing his own article, we get all the issues of a person describing themselves plus the issue of having no reference that could be checked. All the work of Ted Bastin is completely unreferenced. --mfb (talk) 15:51, 12 February 2021 (UTC)

I'm really doubtful that Ted Bastin qualifies as wiki-notable. Nothing I'm turning up would count for passing WP:PROF or WP:AUTHOR; the best source is the Times obit that would only get partway to WP:GNG and that seems to have swallowed some fan remarks uncritically. For example, it mentions the original home of Rupert Sheldrake's work on morphic resonance without saying that Sheldrake's "work" is rank pseudoscience. And it says, The link between quantum physics and information theory, in a broad sense, has grown stronger in recent years, as computer scientists investigate the possibility of quantum physics providing a new basis for computer hardware and, simultaneously, quantum physicists investigate the information basis of their subject. But there is little recognition in recent research of the origin of the latter idea in the pioneering work of Bastin and others. The "and others" does a lot of work there: Bastin himself isn't even a marginal figure in the history of quantum foundations and quantum information. XOR'easter (talk) 17:41, 12 February 2021 (UTC)

H. Pierre Noyes, Ted Bastin, Clive W. Kilmister and H. Dean Brown were all started and largely written by the same user. Brown looks okay, Kilmister is probably relevant but the article doesn't do a good job making that clear. --mfb (talk) 21:55, 15 February 2021 (UTC)

Wikipedia:Articles for deletion/Combinatorial hierarchy --mfb (talk) 21:36, 15 February 2021 (UTC)

Mary Ann Mansigh

deletion discussion

---

Female programmer, co-creator of moldyn method. Yo, we all need to come out for this one, especially if you're in the computational community in phy sci, bigly. Already posted on super- science wp's forum, and several sub-forums as well. It's not certain enough, and too close for my liking. Ema--or (talk) 02:26, 12 February 2021 (UTC)

Sorries all round for my non-NPOV canvas! Ema--or (talk) 21:14, 15 February 2021 (UTC)

Hi, just an issue to discuss. Just wanted to name an issue, which I asked for consultation on, but was not able to get any thing on before the end of discussion. There is the issue of my inconsistencies on Mansigh btw main space and other-space, particularly afd- and Wp project-space, although it is particularly a matter for subjective interpretation. I’d like to end by again apologising for any trouble and thanking anyone who offered any opinion or contribution to the chat, as well as for the space and audience in a place such as this. Bye, ‘til next time. Ema--or (talk) 18:28, 18 February 2021 (UTC)

about Draft:Division by infinity

I don't know where to write a consultation about the article being drafted, so I chose it here. I was wondering if I could create a talk page for the draft space. I think that the harmonic series is related to Draft:Division by infinity. This series diverges to infinity, but in the Basel problem it converges to ${\frac {\pi ^{2}}{6}}$. It seems that this series can be regarded as adding the number divided by infinity from the middle of the sequence, but the calculation result is different. I may have overlooked the boundary between infinity and finite. thanks!--SilverMatsu (talk) 12:52, 7 February 2021 (UTC)

The harmonic series and the Basel series are completely different series! —JBL (talk) 13:34, 7 February 2021 (UTC)

Thank you for your reply. Oops, it was a bit (quite?) strange, as it semms like a Hazel problem in harmonic series in my context. I wrote it with the intention of comparing numbers divided by infinity, but for example, the sum of the reciprocals of prime numbers does not converge, but this may be a problem of the spacing between terms rather than the size of each term.--SilverMatsu (talk) 04:47, 8 February 2021 (UTC)

Can you help convince me that an article entitled "Division by infinity" is needed? Would you also make separate articles entitled "Infinity plus zero" and "Infinity divided by infinity" and "Infinity times zero", etc.? It is quite different from the situation with Division by zero, which is about attempting to apply an arithmetic operation to actual numbers, something that students initially expect to be able to do.

As for the content of the article, about half of the sentences right now seem like pseudo-math, without a precise mathematical meaning. Is there a published article or book that has an exposition similar to the one you are presenting? Ebony Jackson (talk) 08:37, 8 February 2021 (UTC)

Thank you for your reply. Sory, I don't have any helpful literature. In this article, I seems that the meaning of infinity in elementary arithmetic was a monotonically increasing sequence of real numbers. And this article seemed to try to explain what the numbers calculated by Division by infinity are. I tried to compare the example of the calculation result, but I didn't have a concrete idea of ​​how to edit it to improve the article. I tried to help with this article, but it's not working. thanks!--SilverMatsu (talk) 10:57, 8 February 2021 (UTC)

Ebony Jackson makes important points. If you choose to continue to develop this draft, my advice is to (A) locate Wikipedia:Reliable sources and then (B) summarize those sources. I mean, don't wait until later to find sources. Because if you can't find sources, or if your text doesn't reflect those sources, then your work might come across as Wikipedia:Original research, which will not be accepted into the encyclopedia. Best wishes. Mgnbar (talk) 13:14, 8 February 2021 (UTC)

That draft started as a student's class project; I happened across it and took a few stabs at making it into an article but never got far enough that I considered it mainspace-ready. If anyone would like to try, the Beyond Infinity book listed at the end might be a decent place to start. XOR'easter (talk) 14:59, 8 February 2021 (UTC)

XOR'easter thank you for the advice. I will search for references. In the references I have now (I don't have Beyond Infinity) , I can provide related examples, but I am not writing from the perspective of dividing by infinity, so I will continue to search for references. thanks!--SilverMatsu (talk) 13:15, 9 February 2021 (UTC)

I am still skeptical that an article on "Division by infinity" should exist at all. I would suggest that you spend your valuable time elsewhere! Ebony Jackson (talk) 18:47, 9 February 2021 (UTC)

I am also skeptical. But if there are many reliable sources that talk about this concept, saying non-trivial things that aren't covered elsewhere in Wikipedia, then maybe this article should exist. In other words, I think that that part of the discussion also hinges on reliable sources. Mgnbar (talk) 19:17, 9 February 2021 (UTC)

I would be surprised if there were lots of high-quality reliable sources calling out "division by infinity" as a separate topic. You can divide by infinity in some contexts, certainly; the most common is probably the Riemann sphere, which doesn't actually seem to be mentioned in the draft as it stands. --Trovatore (talk) 19:36, 9 February 2021 (UTC)

Mgnbar Thank you for the advice. I would like to lower the priority of this article in my to-do list. If this article can exist as a separate article, I've come to think that references will naturally come together while improving other articles. Thank you for taking your time. --SilverMatsu (talk) 07:03, 10 February 2021 (UTC)

Why not post the article? Looks ready to me.... Ema--or (talk) 02:45, 12 February 2021 (UTC) Still waiting, huh? Ema--or (talk) 22:10, 18 February 2021 (UTC)

Are you interested in writing ${\frac {a}{\infty }}=0$ (a is a finite real constant number) as follows? $x_{n}={\frac {a}{n}},\ \{{}^{\forall }\varepsilon >0,\;{}^{\exists }N\in \mathbb {N} \;\mathrm {s.t.} \;{}^{\forall }n\in \mathbb {N} \;(n>N\Rightarrow |x_{n}-0|<\varepsilon )\}$ It may overlap with the content of (ε, δ)-definition of limit article ...--SilverMatsu (talk) 03:18, 14 February 2021 (UTC)

Zero to the zero power

I would like advice about the lead of the article Zero to the zero power. The question is which of the following should be used as a lead (perhaps the answer is some hybrid of the two).

Possibility 1:

Zero to the power of zero, denoted by 0⁰, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context. In algebra and combinatorics, the generally agreed upon value is 0⁰ = 1, whereas in mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also have differing ways of handling this expression.

Possibility 2:

Zero to the power of zero, denoted by 0⁰, is a mathematical expression that arises most commonly as a value of the function x⁰ or as a limiting form.

• As a value, especially as a value of the constant function x⁰, one has 0⁰ = 1.
• As a limiting form, 0⁰ is indeterminate. This statement means that the limit of a function of the form f(x)^g(x) cannot be determined just from knowing that the limits of f(x) and g(x) are 0: different values are possible, or the limit may fail to exist, depending on what the specific functions f(x) and g(x) are. Because of this, some textbook authors prefer to leave the value 0⁰ undefined, but Knuth and others argue that this is a mistake.

Computer programming languages and software have differing ways of handling the expression 0⁰.

In Possibility 1, many of the same references would be used, just later in the article. (The situation is that one of these was changed to the other one, and then reverted. For the reasons supporting each lead, you can see the history of Zero to the zero power.) Ebony Jackson (talk) 01:51, 10 February 2021 (UTC)

• Possibility 1. It's not acceptable to say that 0⁰ has an agreed-upon value, because it doesn't. --Trovatore (talk) 01:57, 10 February 2021 (UTC)
• Possibility 2. (Full disclosure: I was the one who changed 1 to 2, and Trovatore was the one who reverted it.)

There is a consensus that 0⁰ is an indeterminate form. There is also a consensus that the value of the constant function x⁰ at 0 is 1. These seem to be the useful points from the mathematical literature that this article should focus on. I don't think it is correct to say only that is field-dependent, since for example, in analysis one needs 0⁰ = 1 for the power rule of calculus. I think it is important to distinguish the use of 0⁰ as a value and its use as a limiting form. Ebony Jackson (talk) 02:25, 10 February 2021 (UTC)

That's different, because the exponent in that case is a natural number. When the exponent is a real number, the situation is much less clear. --Trovatore (talk) 02:36, 10 February 2021 (UTC)

It would be helpful to know if there are notable authors who distinguish "0 the integer" from "0 the real number" when deciding whether to define 0⁰, someone at the level of Donald Knuth, who in his 1992 paper argues quite forcefully for disambiguating 0⁰ according to whether it is being used a value or a limiting form, and who says that 0⁰ has to be 1. I think Benson describes the mathematical literature accurately when he writes, "The consensus is to use the definition 0⁰ = 1, although there are textbooks that refrain from defining 0⁰", though he does not have the authority that someone like Knuth has. Ebony Jackson (talk) 02:47, 10 February 2021 (UTC)

There are any number of texts that define $x^{y}$ as $e^{y\log x}$, which is not defined at the point (0, 0). Mostly they don't make a point of noting that this is a different function from the repeated-multiplication function also called exponentiation and notated $x^{n}$, but nevertheless they do not give a definition to the first function at the point (0, 0).

Summary is that Knuth made a reform proposal that has gained some, but not full, acceptance, and Benson is wrong to claim a consensus. --Trovatore (talk) 02:52, 10 February 2021 (UTC)

It can hardly be called a reform proposal: It was Euler that stated that 0⁰ = 1, and he was considering both natural number and real exponents! I would still be happy to know of notable authors (say, notable enough to have a Wikipedia page) who argue as you do, that one defines 0⁰ = 1 when the exponent is viewed as a natural number and undefined when the exponent is viewed as a real number.

In any case, let me see if the following compromise incorporating your comments might be better:

Possibility 3:

Zero to the power of zero, denoted by 0⁰, is a mathematical expression that arises most commonly as a value of the function x⁰ or as a limiting form.

• As a value, especially as a value of the constant function x⁰, the consensus is to define 0⁰ = 1, but there are textbooks that refrain from defining 0⁰ in contexts where real number exponents are involved.
• As a limiting form, 0⁰ is indeterminate. This statement means that the limit of a function of the form f(x)^g(x) cannot be determined just from knowing that the limits of f(x) and g(x) are 0: different values are possible, or the limit may fail to exist, depending on what the specific functions f(x) and g(x) are. This is the reason that some textbook authors prefer to leave the value 0⁰ undefined, but Knuth and others argue that this is a mistake.

Computer programming languages and software have differing ways of handling the expression 0⁰.

No, it's not acceptable to say in Wikipedia's voice that the expression has a consensus value. We can attribute that assertion to Benson if you like, but further down. --Trovatore (talk) 03:32, 10 February 2021 (UTC)

If you don't like to distinguish between 0 the natural number and 0 the real number, think of it instead as distinguishing between the function defined on R×N and the one defined on R_>0×R. --Trovatore (talk) 03:36, 10 February 2021 (UTC)

I think that you-all are ignoring the larger problem — how is exponentiation defined. If we define it with (repeated multiplication) a complex base and natural number exponent, then 0⁰=1. If we define it with (exp and ln) a positive real base and a complex exponent, then 0⁰ is undefined. JRSpriggs (talk) 03:41, 10 February 2021 (UTC)

I totally agree, except that I don't think I was ignoring that :-) . --Trovatore (talk) 03:43, 10 February 2021 (UTC)

Indeed, I think Trovatore's previous comment was essentially that. Trovatore's interpretation is worth including in the article, if there is a source for this by a notable author. Does someone know one?

As for whether there is a consensus that 0⁰, when considered as a value (as opposed to a limiting form), is 1: Maybe it is right that it is not a consensus; if that's the case, we should be able to back that up with modern notable references. So far we have Knuth (and I could also give you books by Lang and others that define x⁰ = 1 even for x = 0). I'd like to see the references that argue that the value 0⁰ (and not just the limiting form) should be left undefined. So far, there have been none provided in this discussion.

I hope that at least we can agree that there are no reputable authors assigning it a specific value other than 1, and that there is a consensus that the value of the function x⁰ at x = 0 is 1. Ebony Jackson (talk) 04:34, 10 February 2021 (UTC)

I don't think Benson's claim is enough to say that there is a consensus.

As for the "function x⁰", I think it depends what you mean. The monomial, yes. But powr is not defined at (0.0, 0.0), no matter whether you start by writing powr(x, 0.0) and then pass 0.0 for x. --Trovatore (talk) 04:48, 10 February 2021 (UTC)

Yes, Benson's claim is not enough; so I was mentioning Knuth and asking if anyone knew similarly notable references that argue that the value 0⁰ (and not just the limiting form) should be left undefined. Ebony Jackson (talk) 05:08, 10 February 2021 (UTC)

No, those others don't assert a consensus, whereas there are lots of sources that simply don't define the value. There is not enough to assert a consensus in Wikipedia's voice. --Trovatore (talk) 05:32, 10 February 2021 (UTC)

I believe you, that such sources exist, but it is not what I believe that matters. I think we would all be happier if someone could list at least one source written by an authority in the field that says not only that the limiting form is indeterminate, but that the value should be left undefined. Ebony Jackson (talk) 05:55, 10 February 2021 (UTC)

I prefer "possibility 1". I do not think the two back to back sentences about what the value is and where it is that value are sufficiently concise (i.e. they are repetitive), but this is a tangential concern. --Izno (talk) 04:41, 10 February 2021 (UTC)

• I also prefer possibility 1. I am not convinced that there is a consensus of algebraists or combinatorists or valuators, as asserted in the other choices, and we should not be picking winners ourselves (here, "teach the controversy" is actually appropriate). —David Eppstein (talk) 06:00, 10 February 2021 (UTC)
• Possibility 1 for now – the first three cited sources show authors who need it to be 1, but don't really establish that there is a consensus that the value is 1. Yes, in certain contexts such as Knuth's combinatorics stuff, it needs to be defined as 1 to be correct, or else lots of nasty hoops need to be jumped through to avoid it. So you need a way to say that: that is some contexts giving it the value 1 makes things correct and easy, while leaving it undefined or giving it any other value makes things wrong or too complicated, so in those contexts it is often taken to stand for 1. But this doesn't need to be in the lead. And thanks for that Knuth paper – a great read like most of his works. Dicklyon (talk) 06:06, 10 February 2021 (UTC)

@David Eppstein: Yes, we should not be picking winners. I too think that it is not right to say that entire fields of mathematics interpret 0⁰ uniformly one way or the other. It is not so much field-dependent as it is context-dependent. (I guess we would all agree that the binomial theorem and the power series for 1/(1-x) are all over math, not really limited to a particular area.)

@Dicklyon: I agree with much of what you wrote. I think it would not be too hard for the lead to broadly identify the contexts in which 0⁰ is defined to be 1, the contexts in which 0⁰ is left undefined (such as when it is a limiting form), and the contexts where there is controversy, whatever they end up being. The details could be left to later in the article, as you suggest. Given the comments that have been made so far, I am no longer happy with either possibility 1 or possibility 2 as written.

It would be nice to have authoritative references beyond Knuth 1992, so that we are not relying only on people's impressions. Thank you, Ebony Jackson (talk) 06:37, 10 February 2021 (UTC)

• possibility 1 seems fine to me.--Kmhkmh (talk) 17:57, 13 February 2021 (UTC)

References

Thank you all for your comments. These are the lessons I have learned from all of you:

• Possibility 2 does not accurately reflect the consensus (at least among the editors here; it would still be nice, however, to have authoritative references beyond Knuth).
• It goes too far in saying that the value of 0⁰ is 1.
• The statement should be limited to contexts in which only nonnegative exponents are being considered. As Trovatore points out, it is helpful to think about there being two different exponentiation functions, one defined on R×N and one defined on R_>0×R. They agree where both are defined, so they could be combined, but not all authors do so.
• Moreover, it would be better, instead of saying that the value of 0⁰ in nonnegative exponent contexts is 1, to say only that the choice to define 0⁰ as 1 is necessary for many standard identities.
• In contexts where real and/or complex exponents are considered, there are authors who say not only that the limiting form 0⁰ is indeterminate, but also that the value 0⁰ should be left undefined. (It would still be good to have an authoritative reference for this. I'd be curious to know, for instance, what the analysis books by Rudin, Spivak, Stein and Shakarchi, Tao, etc., have to say on this if anything, if someone has access to these.)

I will think about whether it is possible to draft a version of the lead that reflects the points you all made. I think it should be possible; maybe one of you would like to try. I don't have time at the moment, but maybe later if no one tries it, I can draft something and ask all of you for feedback again.

Best, Ebony Jackson (talk) 18:57, 12 February 2021 (UTC)

Wow, major props to author(s). What's holding the draft above? It'd make an excellent link to this article. At least, stub, at very least. Ema--or (talk) 22:14, 18 February 2021 (UTC)

AfD and marginal point-of-view pushing

I have nominated 2 × 2 real matrices for deletion. See Wikipedia:Articles for deletion/2 × 2 real matrices, and, please, contribute.

Looking at the incoming links to this article, it appeared that few of them may simply replaced by a link to square matrix, but most reveal a long term point-of-view pushing by fans of the old-fashioned terminology of hypercomplex numbers. This point-of-view pushing consists not only of adding links, but generally also of adding a gibberish that is full of mathematical errors and use of never defined terminology. See my recent edits and the remaining incoming links to 2 × 2 real matrices. So, help would be welcome for fixing the sources of these incoming links. This fix is sometimes difficult, as links to 2 × 2 real matrices are generally used as WP:SUBMARINE for pushing the point of view of hypercomplex numbers, and also as the gibberish use plenty of reference to sophisticated mathematical and physical theories (Lorentz group, general relativity, etc.) that seem irrelevant, although I do not know them enough for being able to decide wheter these references are WP:original synthesis. So, again, help is welcome. D.Lazard (talk) 18:24, 19 February 2021 (UTC)

proposed expansion to MATLAB page

I proposed a draft of an expanded history section for the MATLAB page (mathematics software) here in compliance with WP:COI. I pinged mathematician @Jakob.scholbach: here to see if he would be interested in reviewing the proposed content to ensure compliance with Wikipedia’s rules and principles. He suggested I post here, so here I am! If anyone is willing to take a look at the draft history section, any feedback and/or approval/implementation of some or all of the content would be appreciated. Lendieterle (talk) 18:57, 17 February 2021 (UTC)

Just noting that I looked over the suggested material and added it to the page after making one minor change. Brirush (talk) 03:38, 20 February 2021 (UTC)

S. L. Woronowicz

Shouldn't the article be renamed to Stanisław Lech Woronowicz with full name of the person? --CiaPan (talk) 17:19, 16 February 2021 (UTC)

See WP:COMMONNAME and MOS:BIO — usually we title articles by the most common name for the person (for academics, that might either be the name they publish under, or the form of the name they would use in real life) even though we spell out the full name at the start of the article. I don't have evidence for what version of the name he prefers in real life (for instance, his first name could reasonably be abbreviated either Stan or Stas) but many of his publications (especially the earlier ones) seem to use the initials, so that's a reasonable choice for article title. He has also published as Stanisław L. and Stanisław Lech, though. —David Eppstein (talk) 17:48, 16 February 2021 (UTC)

Not an answer to this question, but there are not a lot of people with this name running around, so it would be natural for three of { S. L., Stanisław, Stanisław L., Stanisław Lech } to be redirects pointing to the fourth. --JBL (talk) 18:00, 16 February 2021 (UTC)

The Polish Wikipedia uses pl:Stanisław Woronowicz, his website just lists his full name, his email address (on the website) uses stanislaw, his arXiv account uses Stanisław. Simply taking firstname lastname might be the best approach here. --mfb (talk) 20:40, 16 February 2021 (UTC)

Keep title. I agree with David Eppstein: Since it seems clear that he prefers to publish under the name S. L. Woronowicz, I think it best to leave that as the title of the article. Then, as JBL suggests, have the variants redirect to that article. Ebony Jackson (talk) 17:13, 17 February 2021 (UTC)

Thank you all for your opinions. I understand the result is to keep the current name. I've put a note about this discussion at the article's talk page. --CiaPan (talk) 11:52, 21 February 2021 (UTC)