Wikipedia talk:WikiProject Mathematics/Archive/2024/Sep

Updates to "Math theorem" Templates: Improved style and new proof parameters

Currently, there are two templates for inserting formatted theorems and proofs into articles: {{Math theorem}} and {{Math proof}} In many cases, however, the proof of a theorem directly follows the theorem. The formatting when juxtaposing these templates is not great, however:

Theorem — My theorem statement.

Proof

My proof statement.

I have written a modified version of {{Math theorem}} (see {{Math theorem/sandbox}}, at [this revision]) to improve the formatting by incorporating the proof as a new parameter for {{Math theorem}}, and also bringing the default formatting of theorems in line with typical math texts:

Theorem. My theorem statement.

Proof. My proof statement.∎

Please join the conversation at Template talk:Math theorem there if you have opinions about the proposed change. The-erinaceous-one (talk) 04:50, 2 September 2024 (UTC)

Can you give examples of articles where you think this template should be used? Personally I find that most of the time ordinary paragraphs are sufficient for theorem statements and proofs (in some articles where authors put theorems in flashy boxes, sometimes with color, etc., I have found the decorations more distracting than helpful). Proofs are helpful in particular in articles that are directly about a theorem or a few theorems, or occasionally in articles where a particular theorem is fundamentally important to the topic, but in cases I'm thinking of collapsing the proofs would defeat the point of including them. Most of the rest of the time I'd skip the proofs altogether (proofs in external resources can be linked from footnotes, or if a proof seems distracting but necessary, it could be put in a footnote in full). –jacobolus (t) 06:35, 2 September 2024 (UTC)

I envision the new version of the template replacing the current {{Math theorem}} template and also being used anywhere else that a formal theorem statement could be useful. As you noted, many pages currently display theorems and proofs in boxes, which I agree are undesirable. Editors might sometimes intentionally add boxes around theorems and proofs, but I think in many cases they simply use {{Math theorem}} because they assume it is the "standard" Wikipedia formatting of theorems. By updating the template, we would improve the formatting across all of those pages that use it and discourage editors from doing ad-hoc formatting of theorems (e.g., boxes and colors).

Regarding the formatting of proofs, I'm not married to the idea of making the proofs collapsed by default, or, in fact collapsible by default. We could choose the default to not make proofs collapsible and then allow editors to enable it using a parameter flag. I am also looking into adding another parameter that allows displaying the proof in a footnote, although I personally find this a worse option than a collapsible box since it requires readers to scroll up and down if they want to see the theorem while reading the proof.

One example of a page that would benefit from a nicely formatted Theorem template is Liouville's theorem (Hamiltonian). Despite the name of the page including "theorem", there is not a formal statement of the theorem. The closest thing it has is

The distribution function is constant along any trajectory in phase space.

but this doesn't state the formal assumptions of the theorem. The-erinaceous-one (talk) 22:58, 2 September 2024 (UTC)

I was looking around for an example of a proof in the footnote, but didn't find one quickly. Here's what I have tried for the {{Math theorem}} template.

Theorem. Mathy mathy math.

The-erinaceous-one (talk) 23:27, 2 September 2024 (UTC)

I would recommend against replacing the previous template, since authors who used it were intending the behavior as provided at the time, not an entirely different appearance chosen by someone else later. I also disagree that Liouville's theorem (Hamiltonian) would benefit from having parts of it wrapped in boxes or reformatted. Ordinary paragraphs are working fine there. In my opinion you should make a new template under a new name if you want it, and then adopt it on pages you write yourself or do significant work on, but should leave other pages alone. Aside: your sandbox version probably has some kind of malformed HTML which causes it to render outside of a colon-indented talk page response (which uses a definition list element). –jacobolus (t) 23:44, 2 September 2024 (UTC)

It looks like the existing template does not work well in lists either. [Edit: I placed an example here, but it broke our ability to use the "reply" editor]. The-erinaceous-one (talk) 00:07, 3 September 2024 (UTC)

Regarding Liouville's theorem (Hamiltonian), I think a weakness of that page is that it is difficult to figure out what "the theorem" actually says. First you have to search through the page to find the quoted text I copied above (which is not clearly labeled as the theorem). Then, you have to reconstruct and/or guess what the assumptions of the theorem are from the rest of the article. The-erinaceous-one (talk) 00:13, 3 September 2024 (UTC)

In other words, it's a typical explanation of something that physicists call a theorem. XOR'easter (talk) 02:31, 3 September 2024 (UTC)

Skimming through links at Special:WhatLinksHere/Template:Math theorem and Special:WhatLinksHere/Template:Math proof, these templates aren't really all that widely used, and in my opinion most of the articles where they are used would be improved by avoiding the templates (and sometimes taking out the proofs). YMMV. –jacobolus (t) 06:51, 2 September 2024 (UTC)

Their usage might not be ubiquitous, but 400+ pages is not insignificant and improving the available template(s) would improve those pages and making nicely formatted theorems and proofs easier. Regardless, the {{Math theorem}} template already exists and is used, so the question is whether the proposed changes would be improvements---not whether we should completely stop using it. The-erinaceous-one (talk) 23:01, 2 September 2024 (UTC)

Also, many of the pages I've opened up use the templates multiple times, so the total number of uses is well over 400. The-erinaceous-one (talk) 00:34, 3 September 2024 (UTC)

Yeah, if it were up to me at least half of those would not have any such template. But it's disruptive to make changes like this at large scale. People should feel free to use this list as inspiration for finding articles which could be improved, including by removing the templates. –jacobolus (t) 01:45, 3 September 2024 (UTC)

I agree with @jacobolus that we don't want to put too much emphasis on proofs. Many articles would actually benefit from removing some of their proofs. This has been discussed multiple times on WPM. From the Proofs section of MOS:MATH: A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgment; as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result. In many cases it would be more beneficial to work on replacing the proofs with some suitable references to reputable sources instead of incorporating them into some new template. PatrickR2 (talk) 03:19, 3 September 2024 (UTC)

Even without the issue of incorporating proofs or not, I often find the current template (and the new template) which wraps the result in a "template box" to be distracting and annoying. In articles that discuss multiple results, it gives undue weight to those that happen to have an official name of "Theorem of Such-and-such" compared with those results that don't. That unnecessarily breaks the flow of exposition. Better use something less intrusive like "Theorem of such-and-such: statement ..." in the text itself. One case where the template could be justified is an article or section dedicated to a single theorem. But most of the time, the use of the template seems misguided to me. PatrickR2 (talk) 03:28, 3 September 2024 (UTC)

References

There are two different matters: how to update the current theorem template and whether its use is appropriate. I commented on the first in the talk page of the template and so here I comment on the second. As someone who actually likes using the template (and the one who actually imported the template from French Wikipedia), I think it depends on how it is used within an article. I agree in some instances, boxes can be jarring especially if there are too many of them. On the other hand, emphasizing a statement in some way is a good idea in some other instances. The axiom of choice articles gives a good example in my opinion: since the article is about a single statement. (As the proof template, I have never used it personally but apparently some people like it) —- Taku (talk) 08:26, 3 September 2024 (UTC)

Square bipyramid proposal to split

Discussion on splitting article the square bipyramid is ongoing. See Talk:Octahedron#Create a square bipyramid or regular octahedron article. More opinions are welcome. Dedhert.Jr (talk) 11:08, 4 September 2024 (UTC)

Help needed on several elementary articles

Farkle Griffen made many edits on several elementary articles including Variable (mathematics), Mathematical object, Indeterminate (variable) and several others. Generally, these article are of low quality, but IMO, most of their edits are disimprovements, as consisting generally of misinterpretations of randomly chosen sources. One of their typical edit is to change the first sentence of Variable (mathematics) from "In mathematics, a variable is a symbol, typically a letter that is used for naming a mathematical object, often a number" to "In mathematics, a variable is a symbol, typically a letter, that holds a place for constants, often numbers".

I must stop to revert them, because WP:3RR, and because of the lack of third party input, I cannot open an ANI thread for disruptive editing (this appears as content dispure).

So, I need some help. D.Lazard (talk) 18:36, 5 September 2024 (UTC)

Mathematical object seems broadly improved. Variable and indeterminate seem tricky to me. There's at least one way these are different, in that variables usually have a domain, while indeterminates are purely formal symbols. (E.g., random variable, real variable, etc.) But many people in casual discourse make no such distinction. Tito Omburo (talk) 18:53, 5 September 2024 (UTC)

Eigenmode vs. eigenmodes (redirects)

Currently,

• eigenmode redirects to Eigenvalues and eigenvectors, and
• eigenmodes redirects to Normal mode.

This is obviously confusing, because eigenmodes ([[eigenmode]]s) and eigenmodes ([[eigenmodes]]) are different link destinations.

Suggestion: the plural redirect [[eigenmodes]] should point to Eigenvalues and eigenvectors, just like the singular version. Thoughts?  — sbb (talk) 03:30, 5 September 2024 (UTC)

The word “mode” (with or with prefix) does not appear at Eigenvalues and eigenvectors; should it? 100.36.106.199 (talk) 10:36, 5 September 2024 (UTC)

I believe that the best way forwards is to look at all of the articles on eigenfunction, eigenmode, eigenstate, eigenvector and normal mode collectively, then discuss what to merge and what to redirect. As part of this, the redirects for singular and plural should be brought into alignment with each other after looking at what links to what.

My first take is that eigenfunctions and eigenvectors should be in the same article, but I could make a case for keeping them separate. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:52, 5 September 2024 (UTC)

Clearly the target of any of these links should not depend on whether it is plural or not. That's easy to fix.

I think Eigenfunction should be kept separate from Eigenvalues and eigenvectors, since the latter article is necessarily focused on linear endomorphisms in general, whereas the former should be focused on the specific application to function spaces. It's fine to leave a summary in Eigenvalues and eigenvectors § Eigenvalues and eigenfunctions of differential operators pointing to Eigenfunction as a main article. –jacobolus (t) 17:25, 5 September 2024 (UTC)

A mode is a standing wave. See eg https://www.feynmanlectures.caltech.edu/I_49.html#Ch49-S5

In mathematical models of wave systems these standing waves appear as "eigenfunctions", also called "eigenvectors" in some representations. A mode, a wave concept, is not a synonym for "eigenfunction", a mathematical concept.

Absent a significant reliable reference, "eigenmode" should be deleted. The word is redundant by repeating itself. Similarly "eigenmodes". Without a reference having these pages is misinformation. Johnjbarton (talk) 15:34, 5 September 2024 (UTC)

According to Eigenmode expansion, eigenmode is a specific term-of-art for solutions of the Maxwell equation along a waveguide. This usage seems to be consistent with many of the hits in a cursory Google scholar search. Tito Omburo (talk) 17:19, 5 September 2024 (UTC)

Thanks, but I disagree with your characterization based on the three sources in that page. None of these references define "eigenmode" and as far as I can tell they only use the word as a modifier as in "eigenmode propagation algorithm".

The solutions to Maxwell's equations along a waveguide seems to be just "modes". Jackson discusses "wave guides" in section 8.3 and says:

• "There will be a spectrum of eigenvalues and corresponding solutions which form an orthonormal set. These different solutions are called the modes of the waveguide.

Here is a review of quantum optics that uses the word 'mode' many times, but 'eigenmode' rarely and inconsistently.

• Fabre, Claude, and Nicolas Treps. "Modes and states in quantum optics." Reviews of Modern Physics 92.3 (2020): 035005.

My guess is that "eigenmode" has a specific technical meaning like you say. But what meaning?

Based on what we know so far, "eigenmode" should redirect to Eigenmode expansion since at least the word is used there. Johnjbarton (talk) 19:38, 5 September 2024 (UTC)

Ok I think I found a review that sorts this out at least for radio waves:

• Huang, Shaode, Jin Pan, and Yuyue Luo. "Study on the relationships between eigenmodes, natural modes, and characteristic modes of perfectly electric conducting bodies." International Journal of Antennas and Propagation 2018.1 (2018): 8735635.
  • Eigenmode expansion method (EEM) [3], singularity expansion method (SEM) [4], and characteristic mode analysis (CMA) [5] are three common modal analysis methods in electromagnetic engineering. The three modal analysis methods result in three different kinds of modes generally, that is, eigenmodes, natural modes, and characteristic modes, respectively.

Based on this reference (and thus restricted to the corresponding field), "eigenmode" is not a synonym for "eigenvector" or "normal mode", but a specialized term related to the "eigenmode expansion method". Johnjbarton (talk) 19:57, 5 September 2024 (UTC)

The edit history for the eigenmode redirect shows that it used to point to Normal mode, but the latest (Oct 2022) edit by Constant314 (talk · contribs) states "Eigenmode is much more general that normal mode. When modes are mapped onto a vector space, a mode becomes a vector. Hence, eigenmode and eigenvector are nearly the same thing", and was changed to point to Eigenvalues and eigenvectors.

I can't comment on whether or not the edit comment is correct, but that was the rationale/statement.  — sbb (talk) 23:22, 5 September 2024 (UTC)

Just some random , unauthoritative thoughts.

• An eigenmode is a mode (whatever that is) that can be mapped onto an eigenvector. More specifically, the numbers that describe the mode can be the components of an eigenvector. Doing that allows the machinery of linear transformations to be used to analyze the mode. Casually speaking, we may say that an eigenmode is a type of eigenvector. Of course, speaking more formally, we mean that the numbers that describe the eigenmode are treated as components of eigenvectors. Again, speaking casually, we say that an eigenmode is an eigenvector, but we do not say that (all) eigenvectors are eigenmodes.

• An electromagnetic field mode is any configuration of the electromagnetic field that satisfies Maxwell’s equations, the constitutive equations, and the boundary values. Solution and mode are used interchangeably. I have not heard the term eigen-solution.

• Mode is not restricted to mean an electromagnetic field mode.

• The voltages and currents of multi-conductor transmission lines are analyzed by the use of eigenmodes.

• It is not an eigenvector unless it is associated with a linear transformation which has an input vector and an output vector.

• The Eigenmode expansion article seems underdeveloped and focused on waveguides. There are no in-line citations in the body of the article. Of the three citations, two are used to establish the name and the other establishes that the method is useful. The external link leads to a not found page. The term eigenmode has been in use since the 1950’s and predats any of the references. I hesitate to redirect anything to this article.

• The Eigenvalues and eigenvectors article is more fully developed. It does not contain the word “eigenmode”, but it does contain “vibrational modes” and maps them to eigenvectors. I have no problem with redirecting eigenmode to Eigenvalues and eigenvectors. Eigenmode is a much broader subject than is covered by the Eigenmode expansion article.

Constant314 (talk) 17:00, 6 September 2024 (UTC)

As far as I know, the level of development of an article is not a criteria for redirects nor are unauthoritative thoughts. My unauthoratative take is that 'eigenmode' is used in different ways in different subfields and mostly as an informal synonym for 'mode' because that does not sound fancy enough.

I have provided a reference that identifies "eigenmode" as a type of "mode". This particular type of mode is discussed in sources listed in eigenmode expansion. So far these are the only source we have that discusses "eigenmode" directly. (Many sources use 'eigenmode' in the sense of 'eigenmode expansion'.) Asserting that 'eigenmode' is a much broader subject and predates the 1950s doesn't really help us here. We can't verify you ;-).

Even with a source that shows 'eigenmode' is an 'eigenvector' representation of a mode, I still do not agree that this redirect to eigenvalues and eigenvectors makes sense. A specialized, modified noun should redirect to the noun, not the adjective. Moreover, all the sources indicate that 'eigenmode' is associated with physics and engineering, not mathematics as topic.

A reasonable alternative to eigenmode expansion could be a redirect to normal mode. Johnjbarton (talk) 17:32, 6 September 2024 (UTC)

I don't think normal mode is a candidate. It is clearly talking about resonances at a fixed frequency. The eigenmodes of a waveguide have a continuous frequency spectrum. Further, it describes a mode as a standing wave. The eigenmodes of waveguides are traveling waves. Constant314 (talk) 21:37, 6 September 2024 (UTC)

Yes, I agree. I think normal mode should be renamed "Mechanical mode" or similar. What if we merge transverse mode and longitudinal mode into eg "Waveguide modes" and add a short section on "eigenmodes"? Johnjbarton (talk) 23:14, 6 September 2024 (UTC)

Of course! We also have Mode (electromagnetism). Bah. Johnjbarton (talk) 23:32, 6 September 2024 (UTC)

I share your frustration. Wikipedia has never been accused of being overly organized. I did not take part in the seminal conversations that established Wikipedia culture, but it seems to have settled to this: verifiability takes priority over completeness which takes priority over avoiding redundancy. You are welcome to reorganize, but don't lose anything. Sound also has longitudinal modes, transverse modes (in solids), and waveguides. You cannot just absorb those into Mode (electromagnetism) or Waveguide modes. However, both of those could use an expanded section on transverse and longitudinal modes. Constant314 (talk) 03:22, 7 September 2024 (UTC)

Redundancy is totally fine in my opinion (and by Wikipedia convention), as long as (1) each subject is encyclopedic ("notable"), (2) the scope of each article is reasonably clear and not entirely overlapping, and the article is reasonably complete and balanced within that scope without putting undue weight on minor aspects of the topic or fringe viewpoints, (3) each article is moderately self-contained and accessible, not dependent on text in other articles, (4) related articles are each correct, don't contradict each-other, reflect the consensus of reliable sources, (5) related articles link to each-other so that readers can find the information they are looking for, and maybe some others I'm not thinking of. With that said though, also feel free to reorganize material by moving it from one article to another, merging articles together, splitting them apart, etc. if a different high-level inter-article organization seems clearer. –jacobolus (t) 04:07, 7 September 2024 (UTC)

I updated Mode (electromagnetism) and included a sentence about eigenmode with the two refs I found. Johnjbarton (talk) 00:51, 8 September 2024 (UTC)

I just made an enquiry at the Teahouse about subpages. Seems that it is not allowed. I was referred to Wikipedia:Splitting. Noit sure if that helps. It looks like your main interest is the eigenmode redirect. Perhaps he should create an eigenmode stub which could point the reader to all the appropriate targets along with some commentary. Does that sound like a good idea? Or, even simple, create an eigenmode dab page. I may go ahead and do that.Constant314 (talk) 18:32, 8 September 2024 (UTC)

I essentially used the page Mode (electromagnetism) for the disambiguation purpose. I think that should be the target for the redirect unless we find a lot more sources and content. We could add an anchor to the paragraph. Johnjbarton (talk) 18:55, 8 September 2024 (UTC)

I am good with that. Eigenmodes is probably a little more general than that, but Mode (electromagnetism) is a probably a good redirect target. You have my support to make the change. I presume that include both eigenmode and eigenmodes. Constant314 (talk) 19:18, 8 September 2024 (UTC)

Thanks,  Done Johnjbarton (talk) 19:39, 8 September 2024 (UTC)

 Courtesy link: Wikipedia:Teahouse § Adding a subpage to an existing article—  jlwoodwa (talk) 20:46, 8 September 2024 (UTC)

Derivative article, again

Sorry, but can someone explain what does the IP say about the numerous references? The IP is known as the former professor, said by itself. Dedhert.Jr (talk) 00:45, 8 September 2024 (UTC)

Just looks like a rant to me, not a real edit request -- there is no concrete proposal to change any particular text to any other particular text that I can see. --JBL (talk) 00:57, 8 September 2024 (UTC)

They do have a point that the Gonnick source is wildly inappropriate. Tito Omburo (talk) 01:30, 8 September 2024 (UTC)

What's inappropriate about it? (Maybe, this discussion should be happening over there.) --JBL (talk) 17:48, 8 September 2024 (UTC)

Wikipedia articles should be based on scholarly sources, not comic books. Tito Omburo (talk) 19:40, 8 September 2024 (UTC)

It's a scholarly source in the format of a comic book. Gonick's three volumes on algebra, geometry, and calculus are each serious about what they cover and don't shy away from hard material; any one of them could be a course textbook. Sure, it makes sense to have multiple citations when a point has been addressed at multiple levels, but I don't see the point of removing citations just because the books they point to are less turgid than average. XOR'easter (talk) 20:58, 8 September 2024 (UTC)

We should probably round out our comic-book references by also citing Prof. E. McSquared's Calculus Primer: Expanded Intergalactic Version. –jacobolus (t) 21:04, 8 September 2024 (UTC)

Tangentially, that seems like a book it might be possible to write an article about, though the reviews I've found so far have been on the short side. XOR'easter (talk) 21:22, 8 September 2024 (UTC)

I'm quite happy with people making the topic entertaining if they're reasonably accurate. But some people think maths has to be po-faced and turgid so I guess another source should be provided as well to cater for them or this complaint will come up again. NadVolum (talk) 20:34, 8 September 2024 (UTC)

This footnote in Kelley comes to mind as an example of humor in a textbook. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:34, 9 September 2024 (UTC)

The sidenotes in Concrete Mathematics are a hoot. note: "What is a proof? 'One half of one percent pure alcohol.'" // "The ∑ sign occurs more than 1000 times in this book, so we should be sure that we know exactly what it means." note: "That's nothing. You should see how many times ∑ appears in The Illiad." // "... now [mathematicians] also have both floor and ceiling [notations]." note: "Next week we're getting walls." // "And the intervals [α..β) and (α..β], which contain just one endpoint, are defined similarly and called half-open." note: "(Or, by pessimists, half-closed.)" // etc. –jacobolus (t) 05:17, 10 September 2024 (UTC)

Not a textbook, but there's also the famous quip about Gauss

References

Category:Pyramids (geometry)

Sorry, but are icosahedral pyramids and gyroelongated square pyramid considered to be part of Category:Pyramids (geometry)? The pyramids are supposed to be a polyhedron in which triangular faces meet their common apex and connect the polygonal base in three dimensions. How are these both supposed to get along with the category, just because they are relatedly constructed by pyramids? I hope someone can explain me before the next edit warring happens again. Dedhert.Jr (talk) 13:01, 12 September 2024 (UTC)

Page move to Piecewise function

After some discussion at Talk:Piecewise_function#Requested_move_20_July_2024, the page Piecewise was moved to Piecewise function. I still consider this decision nonsensical, and the new title highly confusing. For this reason, I'd like to draw your attention to the move. If nobody else has a problem with it, I'll shut up. - Jochen Burghardt (talk) 18:05, 25 August 2024 (UTC)

In addition, a separate(!) DAB page Piecewise property has been created, which links most of its entries (like "Piecewise continuous") back to Piecewise function, where they are explained more or less satisfactorily. According to Piecewise_function#See_also, "Piecewise property" is a generalization of "Piecewise function"! - Jochen Burghardt (talk) 18:05, 25 August 2024 (UTC)

According to WP:NOUN the title should be a noun. For example, instead of "French", articles are titled "French language" or "French people". — Rgdboer (talk) 20:08, 25 August 2024 (UTC)

Or "piecewise property". The problem with "piecewise function" is not grammatical; it is that many of the things defined piecewise are not exactly functions. See e.g. piecewise linear manifold. —David Eppstein (talk) 20:27, 25 August 2024 (UTC)

I'd move Piecewise property to Piecewise, which if someone wants could be upgraded to a "broad-concept article", and leave a separate article at piecewise function, which should ideally contain quite a bit more discussion of piecewise polynomial "splines", piecewise parametric curves as used in CAD/CAM, and so on. –jacobolus (t) –jacobolus (t) 21:33, 25 August 2024 (UTC)

My point is that there is no such thing as a piecewise function. Every function can be defined using if . then . else . endif (linearizing 2dim math terminology), and every function can be defined without it. This is stated correctly in the 2nd lead sentence. In order to subsume also e.g. piecewise linear manifold, what about "Piecewise definition"? - Jochen Burghardt (talk) 21:52, 25 August 2024 (UTC)

every function can be defined without it While this is maybe true in a very narrow pedantic sense, the concept of a "piecewise function" has a clear, obvious, and useful meaning (which is why it is used in practice), and there are valuable things to say about it as a concept which would not be relevant to an article about "every function". –jacobolus (t) 09:27, 26 August 2024 (UTC)

Given a function by its domain, range, and graph, you can check whether it is piecewise linear, piecewise continuous, etc. (provided additional restrictions to domain and range are met). However, I doubt that you can check whether it is piecewise (without any property); I even don't know what that could mean. Moreover, different properties can require different domain decompositions, e.g. $f:\mathbb {R} \to \mathbb {R} ,x\mapsto \min\{1,x^{2}\}$ is piecewise differentiable (use $(-\infty ,1]$, $(-1,+1)$, $[1,+\infty )$) and piecewise monotonic (use $(-\infty ,0]$, $(0,+\infty )$). Also note the absence of any case distinction from this definition.

What we can say, however, is what a piecewise definition is (one that has an outermost case distinction on a domain decomposition into finitely many intervals). Based on this, we can define a function to be piecewise xxx if is has some piecewise definition such that each piece satisfies xxx (this is what the article does). Possible, this can also be generalized from total to partial orders to subsume also David Eppstein's piecewise linear manifold example. - Jochen Burghardt (talk) 13:22, 28 August 2024 (UTC)

Okay, but "take a function and determine whether it is 'piecewise'" is not really something anyone cares much about. Instead, people are interested in proving properties about functions defined or known to be definable in pieces (usually each piece of some specific type, such as constant, polynomial, rational, a linear combination of given basis functions, continuous with bounded derivative, ...), because such functions are extremely common in all sorts of practical applications. Calling these "piecewise functions" is common and well understood (Google scholar turns up 37k results for that phrase – much more common than alternatives I can find, so a good title following WP:COMMONNAME). Deciding that "there is no such thing as a piecewise function" is in my view a semantic quibble that kind of misses the point. –jacobolus (t) 15:54, 28 August 2024 (UTC)

I agree that the term “piecewise property” seems problematic since, unlike continuity or differentiability, it’s not something a function can have or not. “Piecewise-linear” is a property that a space or a function, etc. can have but that’s different. Since other editors have made the same point, I have started a move proposal: “piecewise property” -> “piecewise” at talk:Piecewise_property#Requested_move_26_August_2024. —- Taku (talk) 08:16, 26 August 2024 (UTC)

What about Piecewise-defined property? Surely we agree that a given definition of a property can be piecewise (or not)? The piecewise functions of calculus are perhaps piecewise elementary functions, for example. 100.36.106.199 (talk) 10:37, 28 August 2024 (UTC)

I've been an advocate of piecewise-defined, as grammatically preferable to the other options. Tito Omburo (talk) 10:57, 28 August 2024 (UTC)

Or, if it must be a noun, piecewise definition. —David Eppstein (talk) 17:49, 28 August 2024 (UTC)

+1 for piecewise definition; that seems to get best at the correct concept. Piecewiseness is not a property of functions, but it is a property of definitions. --Trovatore (talk) 19:26, 28 August 2024 (UTC)

Sounds good to me, for the general concept article. Tito Omburo (talk) 19:42, 28 August 2024 (UTC)

Piecewise definition sounds good to me, too. XOR'easter (talk) 02:19, 29 August 2024 (UTC)

Sounds good to me, too. - Jochen Burghardt (talk) 11:52, 29 August 2024 (UTC)

Sure, let's do it. 100.36.106.199 (talk) 16:15, 29 August 2024 (UTC)

Definitely piecewise definition should be the title, and I'm surprised it isn't already. It is the definition, rather than the function itself, that is piecwise. Michael Hardy (talk) 05:50, 13 September 2024 (UTC)

Balinese numerals

The page for Balinese numerals lacks and graphical representation of the numerals so if someone could find some it would be appreciated. Legendarycool (talk) 23:17, 14 September 2024 (UTC)

Unicode mathematical letters block

Hi. Unicode has a Mathematical Alphanumeric Symbols block. For purposes of editing Wiktionary, I'm wondering which of these have set meanings that require their own entries, and which are simply letter variants. For example, using bold letters for vectors is a generic convention, but bold "𝐚" is just a variable without any set meaning, and it can therefore be made a redirect either to 'a' or to a page defining bold variables as vectors. However, ℋ is specifically the Hamiltonian and ℍ (and maybe 𝐇?) are the quaternions, so those should be defined individually.

The Unicode block is too large for me to expect a detailed answer here, but do you know of a reference that might guide me?

I understand that some of the mathematical symbols in Unicode are spurious, or are ad hoc conventions from some source that aren't followed by the mathematical community in general, but it would be nice to define the ones where there is some consensus. (And if there are conflicting consensuses, that's fine, we can always have multiple definitions.)

Again, this is for Wiktionary, but I thought here would be the place to ask. — kwami (talk) 06:54, 12 September 2024 (UTC)

You should definitely not use the unicode ℍ. Use <math>\mathbb{H}</math> instead, giving $\mathbb {H}$. See MOS:BBB. I suspect the same guidance should apply to many of the special unicode mathematics characters. For instance, if it's going to appear in a mathematical equation, the Hamiltonian symbol should probably be <math>\mathcal{H}</math>, ${\mathcal {H}}$, which looks nothing like the unicode to me, so if you mixed the two readers would likely be very confused. —David Eppstein (talk) 07:53, 12 September 2024 (UTC)

For WP, sure, but this is for the purpose of defining the Unicode character.

If the Unicode character doesn't match the <math> display that's supposed to be the same thing, that's presumably an issue with the fonts you have installed: the font called by your browser for a specific Unicode character is different from the font/style called by <math> function. Ideally they should look the same, but there's generally going to be some discrepancy between what we would like the text to look like and what the reader will actually see, unless we post PDF's. Regardless, the underlying data structure will have a use that we would like to define, and AFAIK we can't use <math> to generate entries for Wiktionary. — kwami (talk) 08:19, 12 September 2024 (UTC)

@Kwamikagami Are you sure this is a valuable project? In actual practice, professional mathematicians never use Unicode for mathematical symbols. They almost universally use a variant of Tex/Latex when formatting symbols and equations, corresponding to the <math> tags in wikipedia. PatrickR2 (talk) 19:25, 14 September 2024 (UTC)

Unicode is widely used in mathematical programming, e.g., Lean. And also in domains like industrial mathematics. Tito Omburo (talk) 19:34, 14 September 2024 (UTC)

It seems that in some cases \mathscr is used to display the Hamiltonian symbol. SilverMatsu (talk) 05:47, 15 September 2024 (UTC)

From that thread, if there's a demonstrable contrast between script and calligraphic letters, let me know and we can see about getting them into Unicode. But that may be resolved now - as described at Mathematical Alphanumeric Symbols, there are roundhand and chancery variants of the script letters, which might cover what that thread was calling script vs calligraphic variants. — kwami (talk) 06:34, 15 September 2024 (UTC)

mathscr does not work in the lobotomized version of LaTeX provided by Wikimedia. —David Eppstein (talk) 07:06, 15 September 2024 (UTC)

Ref spam check?

Could someone with more spare minutes than me take a look at this new user's contributions? They have a strong whiff of this to me but I don't have time to properly check. Thanks. JBL (talk) 19:33, 21 September 2024 (UTC)

It looks like this user is in the Albert-László Barabási school of network science. He's a real researcher but also known for some rather exaggerated or pseudo-scientific claims, see e.g. [1]. A textbook on random graphs like Bollobas' will be a vastly more reliable reference than any paper of Barabási's, or most papers in the 'network science' field. When it comes to wiki articles on network science itself, it's ok to use Barabasi's work as a reference. I would avoid it otherwise. Gumshoe2 (talk) 20:17, 21 September 2024 (UTC)

Ok, thanks -- I'm inclined to revert their edits (and have just done so at Graph (discrete mathematics), where they seemed particularly dubious (spammy, NPOV-noncompliant)). --JBL (talk) 20:16, 22 September 2024 (UTC)

That looks like a good revert. The added material was, at best, off-topic. Also, the source removed here was from 2002, pretty much the height of the "scale-free networks" hype era and before the people in that field were adequately scrupulous about things like testing whether a straight-ish line on a log-log plot really is a power law. XOR'easter (talk) 23:21, 22 September 2024 (UTC)

Review of the section "Universal algebra" of the article "Algebra"

The article Algebra is currently a candidate for featured article status. I was hoping to get some more feedback from reviewers. In particular, the 3 paragraphs of the section "Algebra#Universal algebra" need to be assessed for accuracy as the other parts of the article have already been reviewed. The nomination page can be found at Wikipedia:Featured article candidates/Algebra/archive1. Thanks for your time. Phlsph7 (talk) 07:51, 26 September 2024 (UTC)