# Wikipedia talk:WikiProject Mathematics

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To view an explanation to the answer, click on the [show] link to the right of the question.
Are Wikipedia's mathematics articles targeted at professional mathematicians?
No, we target our articles at an appropriate audience. Usually this is an interested layman. However, this is not always possible. Some advanced topics require substantial mathematical background to understand. This is no different from other specialized fields such as law and medical science. If you believe that an article is too advanced, please leave a detailed comment on the article's talk page. If you understand the article and believe you can make it simpler, you are also welcome to improve it, in the framework of the BOLD, revert, discuss cycle.
Why is it so difficult to learn mathematics from Wikipedia articles?
Wikipedia is an encyclopedia, not a textbook. Wikipedia articles are not supposed to be pedagogic treatments of their topics. Readers who are interested in learning a subject should consult a textbook listed in the article's references. If the article does not have references, ask for some on the article's talk page or at Wikipedia:Reference desk/Mathematics. Wikipedia's sister projects Wikibooks which hosts textbooks, and Wikiversity which hosts collaborative learning projects, may be additional resources to consider.
Why are Wikipedia mathematics articles so abstract?
Abstraction is a fundamental part of mathematics. Even the concept of a number is an abstraction. Comprehensive articles may be forced to use abstract language because that language is the only language available to give a correct and thorough description of their topic. Because of this, some parts of some articles may not be accessible to readers without a lot of mathematical background. If you believe that an article is overly abstract, then please leave a detailed comment on the talk page. If you can provide a more down-to-earth exposition, then you are welcome to add that to the article.
Why don't Wikipedia's mathematics articles define or link all of the terms they use?
Sometimes editors leave out definitions or links that they believe will distract the reader. If you believe that a mathematics article would be more clear with an additional definition or link, please add to the article. If you are not able to do so yourself, ask for assistance on the article's talk page.
We try to make mathematics articles as accessible to the largest likely audience as possible. In order to achieve this, often an intuitive explanation of something precedes a rigorous definition. The first few paragraphs of an article (called the lead) are supposed to provide an accessible summary of the article appropriate to the target audience. Depending on the target audience, it may or may not be appropriate to include any formal details in the lead, and these are often put into a dedicated section of the article. If you believe that the article would benefit from having more formal details in the lead, please add them or discuss the matter on the article's talk page.
Why don't mathematics articles include lists of prerequisites?
A well-written article should establish its context well enough that it does not need a separate list of prerequisites. Furthermore, directly addressing the reader breaks Wikipedia's encyclopedic tone. If you are unable to determine an article's context and prerequisites, please ask for help on the talk page.
Why are Wikipedia's mathematics articles so hard to read?
We strive to make our articles comprehensive, technically correct and easy to read. Sometimes it is difficult to achieve all three. If you have trouble understanding an article, please post a specific question on the article's talk page.
Why don't math pages rely more on helpful YouTube videos and media coverage of mathematical issues?
Mathematical content of YouTube videos is often unreliable (though some may be useful for pedagogical purposes rather than as references). Media reports are typically sensationalistic. This is why they are generally avoided.
Why is wikipedia lagging behind the rest of the world in not creating an article on τ (2π)?
The notability of τ=2π is not yet established. Neither the mathematics community nor the math education community has responded to the proposed new constant in any notable way. τ=2π does not at this point of time meet the criteria of notability as per Notability or Wikipedia:Notability (numbers). See also Turn (geometry)#Tau proposal.

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 ${\displaystyle {\frac {\pi ^{2}}{6}}}$ . 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 ${\displaystyle {\frac {a}{\infty }}=0}$  (a is a finite real constant number) as follows? ${\displaystyle x_{n}={\frac {a}{n}},\ \{{}^{\forall }\varepsilon >0,\;{}^{\exists }N\in \mathbb {N} \;\mathrm {s.t.} \;{}^{\forall }n\in \mathbb {N} \;(n>N\Rightarrow |x_{n}-0|<\varepsilon )\}}$  It may overlap with the content of (ε, δ)-definition of limit article ...--SilverMatsu (talk) 03:18, 14 February 2021 (UTC)

## WP:FA devoid of STEM material

STEM articles are extremely underrepresented in WP:FA, and of the few that do exist, many are about products or services, biographical, or otherwise of a non-technical nature. I propose a review of top/high-importance articles in STEM to determine exactly what must be done in order for them to meet the featured article criteria, make appropriate edits, and award them featured article status as soon as possible, without delay. Particularly, material that is fundamental and important to scientific literacy in general or across multiple disciplines. I believe there must be a coordinated effort. Many scientific articles seem to become overly long and disjointed, with so many editors working independently. As a starting point, I think these three articles are all vital to basic scientific literacy and deserve very serious attention: Mean, Function (mathematics), Set (mathematics). My time is limited and I cannot improve them alone, but I would like to be part of such an effort. If at least a couple editors are interested, I'd like to set up an agenda, perhaps with a regular meeting. Once an article is agreed upon, we can read it, report back with comments, discuss how it can be raised to featured article status, and decide on specific edits. AP295 (talk) 20:11, 9 February 2021 (UTC)

I'd like to first establish some consensus about what a given article (starting with Mean) needs to meet WP:FA? standards. Lacking an agenda that interested editors can agree upon, it seems like many efforts to improve technical articles degenerate into content disputes and edit wars. To avoid that outcome, and to make edits productive toward WP:FA?, I humbly ask interested editors to share their suggestions and comments here, or hold their peace when I do edit the article.

• In what ways does the article Mean fall short of meeting WP:FA? criteria?

When I have some time I'll read the article in full and return with my own suggestions/comments. In the meantime, please feel free to share your own. Please make clear, actionable suggestions. AP295 (talk) 13:59, 10 February 2021 (UTC)

I'd also like to link this discussion in that article's talk page. Is there a nicer way to do this in wikimarkup than just pasting the URL? AP295 (talk) 14:06, 10 February 2021 (UTC)

There is a long-term established consensus about what are WP:FA standards (see WP:FA and MOS:MATH). For mathematical articles, there is a further consensus that needs rarely to be explicited: a mathematical article requires to be mathematically correct. So, opening a general discussion on that (I do not talk of a discussion on a specific point) is a waste of time for every participant to this discussion. So, I strongly suggest to close it immediately. D.Lazard (talk) 15:35, 10 February 2021 (UTC)
Please make clear, actionable suggestions about developing/improving the article Mean. AP295 (talk) 15:38, 10 February 2021 (UTC)
The article Mean illustrates the difficulty mathematics articles have in getting to WP:GA or WP:FA standard. If we read the lead of the article we come across this formula ${\displaystyle {\displaystyle \mu =\sum xp(x)....}}$ . That will instantly trigger a too-technical complaint from a reviewer. The whole intro is packed full of technical terms. For an example take this quote from Wikipedia:Featured article review/Euclidean algorithm/archive1
So, considering that the article has been quite substantially rewritten since it passed FAC, and the version that passed FAC was decipherable at least in English, I suggest that the first step towards preserving Featured Status here is a revert to that version. Making math digestible is not rocket science: textbooks and other websites do it all the time-- we can, too.
This comes from User:SandyGeorgia who is quite involved in the FAC process.
Unfortunately she is wrong. Making maths decipherable and digestible is very hard, some brave souls have managed it and any FA takes a lot of time to produce. The textbooks and website she mentions manage to make small parts of a whole topic digestible, but fail the other FAC of comprehensive: it neglects no major facts or details and places the subject in context;. And there are parts of the mean article with some quite complex major facts. This tension between digestible and technically correct and comprehensive make any STEM topics a tricky one for FA. Others in the project have had much more success with getting articles through GA and it is a more achievable task. --Salix alba (talk): 17:47, 10 February 2021 (UTC)
The mean is an uncomplicated concept and will lend itself to an uncomplicated wiki article with a bit of work. AP295 (talk) 19:27, 10 February 2021 (UTC)
Regarding sigma notation, I think we can avoid it in the introduction in favor of using something like (a1 + a2 + ... + an)/n or p1 a1 + ... + pn an, but possibly make use of it when needed in the body of the article. The intro should be accessible to the casual reader and the body can include more technical content (and the notation that comes with it) for completeness. AP295 (talk) 19:57, 10 February 2021 (UTC)
I don't think the concept of average is simple. Claiming that Grandi's series is ${\displaystyle {\frac {1}{2}}}$  is also average in a sense. 1 − 2 + 3 − 4 + ⋯ cannot be averaged by the Cesàro mean. These are, in a sense, averages, claiming that the averages cannot always be defined.--SilverMatsu (talk) 00:13, 11 February 2021 (UTC)
That's kind of neat, but probably outside the scope of the article. I think Arithmetic mean, Expected value, Average could be merged into a single article. Most people are probably looking for expected value, and it should be given due weight. Currently, Mean is really just a laundry list of various things that people call a "mean", so I'm not exactly sure what to do with it or whether our efforts might be better spent cleaning up and merging the former three. The replies so far have been tepid at best and I'll be pretty busy with other work for a while but I'll leave this RfC open and try to make time at some point. AP295 (talk) 01:50, 11 February 2021 (UTC)
• Misplaced RFC. The place to discuss whether an article (that you think meets FA standards) actually does is in an FA nomination. The place to discuss how to improve that article (whether up to FA standards or otherwise) is on the talk page of the article. Whether the FA standards actually work or can be made to work for mathematics content (as in Salix alba's comment above) is a broader topic that is more appropriate here. As SA says, it has been possible to get even quite technical articles through the Good Article review process. It still takes significant efforts to make the mathematics understandable but there is a greater likelihood of that effort being rewarded. As Mean is not currently GA, that step seems like it should go first. To my mind it is not yet close to GA (it's rated B but I think it's more like C, mostly because it is too haphazard and has a lead that is entirely about one thing but a body about something else) but other GA reviewers might disagree. —David Eppstein (talk) 18:27, 10 February 2021 (UTC)
I do not think it meets FA standards. When it gets to that point, I'll take it up with the folks at FA nomination. I was going to make a topic on Mean's talk page too once we have a general idea of what must be done, but as the problem concerns more than just one article, I believe this is a good staging area. AP295 (talk) 18:58, 10 February 2021 (UTC)

Part of the problem I'm seeing is that Mean, Arithmetic mean, Expected value, and Average are four separate articles, with a lot of redundant content between them. There must be a better way to organize this information, preferably into a single article, or a couple of articles at most AP295 (talk) 01:59, 11 February 2021 (UTC)

Let's not forget centroid and center of mass. —David Eppstein (talk) 02:06, 11 February 2021 (UTC)
I can't tell if you're being a smartass or not. At the very least, Arithmetic mean, Expected value, and Average could probably be integrated into a single article. There's a lot of redundancy between the three and having them in a single article would make their relation clearer. Less is more, sometimes. AP295 (talk) 02:12, 11 February 2021 (UTC)
Actually, the articles Average and Mean seem to be trying to do the same thing, so they could be put together. Merging Expected value and Arithmetic mean into a single article would probably work fine as well. All four are a mess and need a lot of work, even if they are to remain four separate articles. AP295 (talk) 02:42, 11 February 2021 (UTC)
I would oppose a merge of Average and Mean. The common name "average" is broader than "mean", not just technically (since "average" can refer to other measures of centrality) but also in not-explicitly-mathematical applications, where averages are often a rough description of centrality in a concept that isn't precisely quantified. The page Average needs a lot of work, but much of that work should build out meanings that aren't redundant with the content at Mean. - Astrophobe (talk) 02:53, 11 February 2021 (UTC)
There's also central tendency, which shares plenty of content with the others. The articles centroid and center of mass are different from what we're talking about here, so I'm not considering them at the moment. "The page Average needs a lot of work, but much of that work should build out meanings that aren't redundant with the content at Mean." I think that would be difficult. Do you think there's any way to condense Average, Mean, Expected value, Arithmetic mean and central tendency into fewer than five articles? And if not, how should we define the scope of each article? AP295 (talk) 03:38, 11 February 2021 (UTC)
In what sense are centroid and center of mass different? They are the same as the expected value of a uniform distribution over the shape they are defined over, for instance. And the centroid is certainly in wide use as a central tendency. But we do need to distinguish the general idea of a mean, center, or central tendency from the specific additive versions described in average and expected value. —David Eppstein (talk) 04:56, 11 February 2021 (UTC)
That's fine, but then how should the article Mean be written differently from Average? Part of the challenge seems to be in agreeing upon the scope of any given article. AP295 (talk) 05:32, 11 February 2021 (UTC)
For example, is the table "Expected values of common distributions" in Expected value necessary? And I do like that it includes a few proofs, but as far as I know there isn't supposed to be any collapsed-by-default content in articles. AP295 (talk) 05:45, 11 February 2021 (UTC)
Centroid assumes a uniform mass distribution; center of mass does not necessarily. Dicklyon (talk) 19:54, 11 February 2021 (UTC)
@Dicklyon: DE meant "In what sense are centroid and center of mass different [from what we are talking about here]?", not "... different [from each other]?" (It is a response to the comment by AP295.) --JBL (talk) 19:56, 11 February 2021 (UTC)
That's what I get for reading from the bottom instead of the whole conversation. Sorry. Dicklyon (talk) 01:02, 12 February 2021 (UTC)
Dick, YOU'RE FIRED! My point was that those articles are pretty distinct from Average, Mean, Expected value and Arithmetic mean which have a lot of duplicate and/or unnecessary content and do not adequately distinguish themselves from the others. It's fine to keep them separate, I have no problem with that, but then we should try to make them clearer and more concise so that the reader understands the distinction, and the relation, between those concepts. AP295 (talk) 15:22, 12 February 2021 (UTC)
Have a look at the Average article. I think it might stand a better chance of getting promoted than mean. Its aimed more at a general reader, has less technical details. FA encourages summary style and the Average article already uses that quite a lot. --Salix alba (talk): 01:00, 12 February 2021 (UTC)
I don't believe "summary style" necessarily means "non-technical". WP:FA? is a very general and concise standard of quality, and to me it sounds like a cop-out when people claim that it disfavors technical or scientific articles. AP295 (talk) 19:59, 12 February 2021 (UTC)
And in fact, Principal component analysis, the first article I ever edited, is a good example of something that could be written much more concisely. I attempted to do just that but didn't get much past the lead, though at least I was able to improve it somewhat. It's not so much that these articles can't be written in summary style, but at least half the time I try to remove anything or reorganize/reword content in an article, other editors come out of the woodwork and go apeshit. That is part of the reason we're having this RfC, so that we can all get on the same page instead of getting into a week-long brawl that ends up on WP:ANI. I don't have the time for that bullshit. AP295 (talk) 17:07, 13 February 2021 (UTC)

I'd much prefer making Addition a featured article. I actually used to edit a ton of Wikipedia math articles, and got a few to GA status. I thought I'd try a crack at a featured article. I got one reviewer who suggested reference changes. I made all those changes, then the FAC was rejected after 8 days because no one cared to review it. Honestly, that's one of the biggest reasons I stopped editing.

Anyway, addition should be much easier to get to FA status.Brirush (talk) 22:01, 11 February 2021 (UTC)

Most people know how to add and generally have a firm understanding of the concept. Certainly it's a worthy objective, but I'm mostly concerned about articles that the undergraduate student might depend upon, many of which are in pretty rough shape. I don't think silly stuff like the value of .9 repeating (which has a FA) or zero to the power of zero (see the section below) or division by infinity (above) provide as much value to the young student/scholar as a good Set (mathematics) article would, for instance. I admit I did not anticipate when I made this RfC that Mean and its related articles would together comprise such a nasty rat-nest of redundant and disorganized content, which nobody wants to touch, so perhaps Set (mathematics) would be a better place to start. AP295 (talk) 22:41, 11 February 2021 (UTC)

For Set (mathematics), the set operations should be explained much earlier than they are. The article has a lot of sections and it can probably be reorganized into fewer. The first image in the article is not particularly informative or instructive, and so I'd like to replace it with something a bit more useful. This article should not be hard to get to WP:FA status, most of the content is already there and with some adjustments it should be a great article. Unless anyone has a good plan for mean and its related articles, the set article will be a better warm-up. AP295 (talk) 15:43, 13 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.[1][2][3]
• As a limiting form, 00 is indeterminate.[4] This statement means that the limit[5] 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[6][7] prefer to leave the value 00 undefined,[2] but Knuth and others argue that this is a mistake.[3][8]

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 ${\displaystyle x^{y}}$  as ${\displaystyle e^{y\log x}}$ , 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 ${\displaystyle x^{n}}$ , 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,[1][2][3] but there are textbooks[9][10] that refrain from defining 00 in contexts where real number exponents are involved.
• As a limiting form, 00 is indeterminate.[4] This statement means that the limit[11] 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,[2] but Knuth and others argue that this is a mistake.[3][8]

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

1. ^ a b Leonhard Euler; J. D. Blanton (transl.) (1988). Introduction to analysis of the infinite, Book 1. Springer. ISBN 978-0-387-96824-7., Chapter 6, §99, p. 76.
2. ^ a b c d "The choice whether to define 00 is based on convenience, not on correctness. If we refrain from defining 00, then certain assertions become unnecessarily awkward. [...] The consensus is to use the definition 00 = 1, although there are textbooks that refrain from defining 00." Donald C. Benson, The Moment of Proof : Mathematical Epiphanies. New York Oxford University Press (UK), 1999, p. 29. ISBN 978-0-19-511721-9
3. ^ a b c d Knuth, Donald E. (1992). "Two Notes on Notation". The American Mathematical Monthly. 99 (5): 403–422. arXiv:math/9205211. doi:10.1080/00029890.1992.11995869.
4. ^ a b Augustin-Louis Cauchy, Cours d'Analyse de l'École Royale Polytechnique (1821), pp. 65-69. In his Oeuvres Complètes, series 2, volume 3.
5. ^ Here all the limits are as x approaches a real number or ±∞, from one side or both sides, and f(x) is assumed positive on each relevant side so that f(x)g(x) is defined.
6. ^ Edwards and Penney (1994). Calculus, 4th ed, Prentice-Hall, p. 466.
7. ^ Keedy, Bittinger, and Smith (1982). Algebra Two. Addison-Wesley, p. 32.
8. ^ a b "Some textbooks leave the quantity 00 undefined, because the functions x0 and 0x have different limiting values when x decreases to 0. But this is a mistake. We must define x0 = 1, for all x, if the binomial theorem is to be valid when x = 0, y = 0, and/or x = −y. The binomial theorem is too important to be arbitrarily restricted! By contrast, the function 0x is quite unimportant". Ronald Graham; Donald Knuth; Oren Patashnik (1989-01-05). "Binomial coefficients". Concrete Mathematics (1st ed.). Addison Wesley Longman Publishing Co. p. 162. ISBN 0-201-14236-8.
9. ^ Edwards and Penney (1994). Calculus, 4th ed, Prentice-Hall, p. 466.
10. ^ Keedy, Bittinger, and Smith (1982). Algebra Two. Addison-Wesley, p. 32.
11. ^ Here all the limits are as x approaches a real number or ±∞, from one side or both sides, and f(x) is assumed positive on each relevant side so that f(x)g(x) is defined.

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)

## 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

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)

## 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)

## 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 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)

## 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)

## Uniform Boundedness Conjecture

We now have an article Uniform Boundedness Conjecture, and a redirect uniform boundedness conjecture pointing to torsion conjecture. They're both on finiteness of sets of points in arithmetic geometry but one is on torsion points and the other is on rational points. Can someone who understands the relations among these principles help clean up this duplication of titles, please? —David Eppstein (talk) 21:16, 22 February 2021 (UTC)

There are now several conjectures in arithmetic geometry that are called the "uniform boundedness conjecture", which all have essentially the same origin. To my understanding, the uniform boundedness conjecture about torsion points at torsion conjecture by Ogg (1973) was the starting point. After the proof of the Mordell conjecture by Faltings in 1983, the adaptation to rational points (which include the torsion points over the rationals) at Uniform Boundedness Conjecture was the next generalization. Now, there is also the uniform boundedness conjecture in arithmetic dynamics posed by Morton and Silverman in 1994.
They are all known by the name "uniform boundedness conjecture", but they are often specified (e.g. Uniform boundedness for rational points). I would suggest:
Plus, it might be useful to make redirects at similar titles (e.g. Uniform boundedness conjecture (torsion points), Uniform boundedness conjecture (rational points), Uniform boundedness conjecture (arithmetic dynamics)). I also would not be surprised if there are other uniform boundedness conjectures (e.g. following the Uniform boundedness principle). — 21:59, 22 February 2021 (UTC)
That sounds reasonable. By the way, Ogg's conjecture on torsion of elliptic curves over Q was essentially formulated earlier by Beppo Levi at the 1908 ICM, and then again by Trygve Nagell in 1952. See the article "Beppo Levi and the arithmetic of elliptic curves" by Schappacher and Schoof. Ebony Jackson (talk) 05:50, 23 February 2021 (UTC)
Just carried out the proposal and added the background on Levi and Nagell to Torsion conjecture as well! — 09:11, 25 February 2021 (UTC)