Wikipedia talk:WikiProject Mathematics/Archive/2021/Nov

Homogeneous relation
Wikipedia has an article Homogeneous relation ("In mathematics, a homogeneous relation (also called endorelation) over a set X is a binary relation over X and itself..."). See also. I don't have access to the sources given. However, I have never seen this use outside of Wikipedia, and other Wikipedians have commented about this as well on Talk:Homogeneous relation. Is this term really used this way? –Tea2min (talk) 13:09, 2 November 2021 (UTC)
 * It seems so Quart. J. Math. Oxford (2), 28 (1977) 31-39, but I agree it is not a common usage. -- 22:22, 2 November 2021 (UTC)
 * There are also at least two other uses of the term, albeit in context - In algorithmic complexity, one sometimes talks of "homogeneous relations" with a meaning coming from homogeneous equation, and Fraisse (in the book 'Theory of Relations' that is actually cited in the current article on homogeneous relations) uses homogeneous with a meaning coming from the homogeneous model of model theory. Felix QW (talk) 10:34, 3 November 2021 (UTC)
 * Thanks. —Tea2min (talk) 06:46, 4 November 2021 (UTC)
 * For what it's worth, besides Talk:Homogeneous relation there is some more relevant discussion at Talk:Binary relation, Talk:Binary relation and Talk:Binary relation. Anyway, there are sources, so that's fine. I just don't think the term should be used in other articles, however. —Tea2min (talk) 10:14, 4 November 2021 (UTC)
 * Do you have a more common suggestion for the article name? I saw (e.g. in Davey.Priestley.1990, Introduction to Lattices and Order) "relation on a set" for "homogeneous relation"; however, I find the distinction "homogeneous" vs. "heterogeneous" easier to grasp than "on a set" vs. (say) "between two sets"; moreover, "on a set" can hardly be turned into an article name. Anyway, not being a native English speaker, I can't really judge on naming issues. - Jochen Burghardt (talk) 10:38, 4 November 2021 (UTC)
 * "Relation on a set X" would be my preference for a subset of X×X. It's what the sources I know of use. (Note: Relation on a set redirects to Binary relation. I created that redirect myself some time ago.)
 * Many books use a "zeroth" chapter to establish the nomenclature used in the rest of the work, any many of them only need to mention (binary) relations at one point in that chapter and then immediately go on and define derived notions like "domain", "codomain", "function", "graph", "preorder", "partial order" etc. without ever needing to use the terms used for the most general definitions of relations ever again. I guess that's the reason why terms like "homogeneous relation", "heterogeneous relation", "finitary relation" etc. are not used much in the literature. (Or rather, in the literature I have seen.)
 * Every person with some mathematical training can probably guess the meaning of "homogeneous relation" when they encounter it the first time. There are other notions like left-unique/right-unique and left-total/right-total with the same problem: Few books ever need to define terms like these (simply because you don't need them that often), and you can probably guess their meaning when you first see them, so they don't feel wrong. And yet I would not call them common.
 * I see a similar problem with the terms serial relation/connected relation/total relation. I understand the need to distinguish between "serial" and "connected". And yet I stumble when an article uses "serial" or "connected" when every source I have ever seen used "total". Anyway, as a reader I would prefer if our articles would not use terms that are not commonly used in the (relevant) literature. —Tea2min (talk) 11:23, 4 November 2021 (UTC)

Economic
Meaning of economic 105.112.177.152 (talk) 18:17, 4 November 2021 (UTC)
 * Please be more specific. — MarkH21talk 18:20, 4 November 2021 (UTC)

Hat operator
Any idea what to do with this? Tagged for no citations in 2007 and none added since then; its contents might better fit with the title "several mostly unrelated uses of the circumflex in mathematical contexts". --JBL (talk) 02:33, 5 November 2021 (UTC)
 * A solution would be a redirect to a (non-existent) entry in Glossary of mathematical symbols. However, for writing this entry, one should take care that
 * The section "Quantum mechanics" is not about the hat operator
 * The use for cross product is rare. So this use must either be ommitted or it must be claerly stated that it is not common
 * The sections "Estimated value", "Hat matrix" and "Linear algebra" refer to very close uses
 * The use for the completion of a ring is lacking
 * D.Lazard (talk) 09:37, 5 November 2021 (UTC)

Reducing subspace
I have created a new article titled reducing subspace. Michael Hardy (talk) 22:11, 25 October 2021 (UTC)
 * Which articles should link to it? (There are now four, all of the links having been created by me.)
 * What else should be done toward its improvement?
 * I would say it needs to be explained so that a reader without a PhD in linear algebra can understand its contents-- Wikipedia is not a textbook or scientific journal after all, but I'd make a similar criticism of about 80% of the mathematical articles on Wikipedia. Reyk YO! 08:33, 26 October 2021 (UTC)
 * "Ph.D. in linear algebra" is hyperbolic and sarcastic. Avoiding things like that might make it easier for people to communicate with you. Very many undergraduates in fields other than mathematics should be able to understand what I wrote. Obviously more can be added that will aid with understanding, including some concrete examples. Michael Hardy (talk) 18:10, 26 October 2021 (UTC)
 * And I would add that the initial context-setting phrase "In linear algebra" tells the reader in advance that some acquaintance with that subject is assumed. Michael Hardy (talk) 18:12, 26 October 2021 (UTC)
 * This article as written should be understandable by anyone who has taken a good sophomore-level undergraduate class in linear algebra. There is a genuine issue with the level at which our mathematics articles are written, but attacking an article that any math major should be able to read and understand as incomprehensibly inaccessible says more about the complainer than the article in question.  "PhD in linear algebra" really. --JBL (talk) 12:23, 26 October 2021 (UTC)
 * I'm not sure why advocating that articles be written for the average reader means I should get called names, but I'm not going to rise to the bait. Reyk YO! 12:28, 26 October 2021 (UTC)
 * Because what you actually did was make an unhelpful, overbroad, and misinformed complaint about mathematics articles (ergo writers of mathematics articles) generally. Modern linear algebra is an amazing human accomplishment; in order to engage with it, people do actually need to know some prerequisite material, namely, a couple of courses of mathematics beyond what is taught in a good high school curriculum.  Any possible article on reducing subspaces will have a barrier to readership like that; given the context, the draft Michael Hardy has written is not particularly inaccessible, and your comments are useless for increasing accessibility.  If you don't want to engage in arguments with a high ratio of insult to substance, you shouldn't start them. --JBL (talk) 12:48, 26 October 2021 (UTC)
 * I mean for chrissakes do you not realize that "written like a journal article" and "written like a textbook" are diametrically opposed in the context of mathematics writing? Your initial comment is content-free whining. --JBL (talk) 12:51, 26 October 2021 (UTC)
 * I would like to acknowledge that the tone of my comments above is excessively confrontational, and I have apologized to Reyk for such on their talk-page. --JBL (talk) 13:24, 26 October 2021 (UTC)
 * (ec) Aight, let's try again. I may be expressing myself poorly. My opinion is that even articles on very technical subjects could and should be written in such a way that the average reader can get an idea of what the subject is about. There shouldn't be many, if any, articles on Wikipedia that you need to have taken university courses to even engage with. Otherwise my feeling is that articles like that are too specialised, too "jargony", for a general encyclopedia. Reyk YO! 13:31, 26 October 2021 (UTC) Addendum: I also want to say that the overly technical and often very inscrutable way mathematics articles are written here is something I've meant to bring up for a while, and I don't want to imply that this particular one is any better or worse than the others.
 * While I don't feel that 's expectations to mathematical encyclopedia articles are satisfiable, I'd agree with him that the article is very concise. It could at least take an example (for a 3×3 matrix, say, preferrably with a geometrical interpretation that can be illustrated in an image), an indication of possible applications (apparently in statistics), some history (if known: who used it first, and for which purpose). Does the concept generalize to infinite dimensions? n and r should probably be unified? Ir is the r×r unity matrix? "orthogonal complement" should be linked (and not typeset in math). Are there neccessary or/and sufficient conditions for the existence of a reducing subspace, given r and M? - Jochen Burghardt (talk) 11:58, 26 October 2021 (UTC)
 * Yes, the biggest issue with this stub article is that it provides no motivation or context. The notation and level of abstraction may be fine for the kind of readers who will stumble across this page, but even many readers who can read it are going to be mystified about the purpose. –jacobolus (t) 18:36, 26 October 2021 (UTC)
 * I have fixed a couple of typos (the n versus the r, and a copy of r-by-r that should have been r-by-1), broke up the so that orthogonal complement could be linked, and defined the identity matrix. An example would be the natural next piece of prose to add. --JBL (talk) 12:58, 26 October 2021 (UTC)
 * This seems like slightly nonstandard and confusing notation: $$\mathcal R\subseteq\mathbb R^{r\times1}$$. A subspace $$\mathcal R$$ of $$\mathbb R^r$$ might be represented using using any linearly independent basis of $$k \leq r$$ vectors in $$r \times k$$, but the $$r\times1$$ here in conjunction with $$\subseteq$$ is going to confuse at least some people. I’d stick to the notation and definitions from e.g. http://users.stat.umn.edu/~rdcook/RecentArticles/CLC.pdf: a subspace $\mathcal R$ of $\mathbb R^r$ is an invariant subspace of $\mathbf M \in \mathbb R^{r\times r}$ if $\mathbf M\mathcal R \subseteq \mathcal R$; so $\mathbf M$ maps $\mathcal R$ to a subset of itself. $\mathcal R$ is a reducing subspace of $\mathbf M$ if, in addition, $\mathbf M\mathcal R^\perp \subseteq \mathcal R^\perp$. –jacobolus (t) 22:04, 26 October 2021 (UTC)
 * I would instead write the lead as something like: “In linear algebra, a reducing subspace $$\mathcal R$$ of a linear map $$\mathbf T$$ from a vector space $$\mathcal V$$ to itself is an invariant subspace of $$\mathbf T$$ whose orthogonal complement $$\mathcal R^\perp$$ is also an invariant subspace of $$\mathbf T.$$ That is, $$\mathbf T(\mathcal R) \subseteq \mathcal R$$ and $$\mathbf T(\mathcal R^\perp) \subseteq \mathcal R^\perp.$$” –jacobolus (t) 23:35, 26 October 2021 (UTC)
 * Here is a good example of a clear definition along these lines: Hosack (1970) “On when Invariant Subspaces of Unbounded Normal Operators are Reducing”. –jacobolus (t) 00:04, 27 October 2021 (UTC)
 * Your proposed lead is certainly much clearer to me than the current one. —David Eppstein (talk) 00:52, 27 October 2021 (UTC)
 * Apparently the concept of “reducing subspace” is older than these recent works. Searching the literature turns up a bunch of papers dating back to the 60s about operators in Hilbert spaces. There (e.g. in Halmos, 10.1515/crll.1961.208.102) a reducing subspace is defined as: “A subspace $$\mathfrak M$$ reduces an operator $$A$$ if and only if the projection on $$\mathfrak M$$ commutes with A. –jacobolus (t) 22:08, 26 October 2021 (UTC)

I rewrote the definition as suggested previously, and did some other reworking of the article. It is still lacking in references, context, etc., but hopefully a bit clearer. What do folks think? Reducing subspace. –jacobolus (t) 16:43, 5 November 2021 (UTC)

Linear recurrence relations
Another thing to file under "this can't be right but I don't know what to do about it": Should they all point to Constant-recursive sequence? (But really is there no treatment of linear-but-not-constant-coefficient recurrences anywhere on Wikipedia?) --JBL (talk) 02:38, 5 November 2021 (UTC)
 * Linear recurrence redirects to Linear difference equation
 * Linear recursive sequence redirects to Constant-recursive sequence
 * Linear recursive sequences redirects to (a non-existent section of) Recurrence relation
 * Maybe all but the last subsection of Recursive sequence? A well-written stand-alone article might help, but it looks like there are too many similar overlapping articles already. There's also P-recursive equation, which is not general enough for these redirects, but is still "linear" in this sense (this linearity is not what I usually think of as being "linear"). — MarkH21talk 03:39, 5 November 2021 (UTC)
 * We have also Recurrence relation and Linear difference equation which consider the linear case with constant coefficients in details, and Holonomic function, which gives much information on the linear case with polynomial coefficients, which is lacking in P-recursive equation.
 * It seems that, except for some trivia, the theory of recurrence relations is reduced to two cases:
 * Linear with constant coefficient: this case is detailed in too many articles
 * Linear with polynomial coefficients: this case is badly described in WP, probably because the theory is relatively recent
 * So, I suggest to reduce the subject to only three articles
 * Recurrence relation for generalities and summary of the two main cases
 * Linear recurrence with constant coefficients
 * Linear recurrence with polynomial coefficients
 * D.Lazard (talk) 10:49, 5 November 2021 (UTC)
 * That looks like a decent suggestion to me. — MarkH21talk 17:51, 5 November 2021 (UTC)
 * To me also. The new names look better; I wouldn't have thought to look for "Constant-recursive sequence" rather than "linear recurrence relation". Also I think it is important to use "recurrence" rather than "recursive" because recursive has too many other not-closely-related meanings (computable, in recursion theory, or programmed using a function that recursively calls itself, in computer programming). —David Eppstein (talk) 22:30, 5 November 2021 (UTC)
 * I also agree. Moreover, "linear recurrence relation" seems much more common than "constant-recursive sequence". XOR&#39;easter (talk) 15:50, 7 November 2021 (UTC)

Ramanujan machine
It's an article that was previously discussed in AfD, so I'll write a note just in case. see Ramanujan machine and Articles for deletion/Ramanujan Machine.--SilverMatsu (talk) 04:43, 13 November 2021 (UTC)

I fixed list of references. Given that the previous AfD was closed on 14 February 2021, the newly added references are probably the 6th and 7th references.--SilverMatsu (talk) 15:20, 13 November 2021 (UTC)

Our main article
I am in course of rewriting Mathematics. My main purpose is to make it mathematically oriented instead of being philosophically oriented. See Talk:Mathematics for details on my motivation and my guidelines for this job. My edits may be considered as WP:original synthesis, but I do not see any way for avoiding this.

I have just added an empty section on "Discrete mathematics". For filling it, I could paraphrasing the lead of Discrete mathematics (this is one of the best leads for our articles on mathematics areas). But, the work could certainly better done by a specialistsuch as.

Also, section "Calculus and analysis" is still in its old state, and we need a section on "Probability, measure theory, and statistics". Help would be welcome for these sections.

Help would also be welcome for still improving the sections that I have already rewritten. I guess that they are not so bad, if I consider the few reactions of the 2300 watchers of the page. D.Lazard (talk) 15:40, 13 November 2021 (UTC)
 * The article is certainly improved already; the only qualm I have with the changes is the presence of Mathematics Subject Classification numerical codes in the prose. User:力 (powera, π,  ν ) 16:49, 13 November 2021 (UTC)

Talk page
An anonymous user suggested somewhere that the equation 3^a = 2^b + 1, a and b positive integers, only has the solutions a = b = 1 and a = 2, b = 3. Does someone know where this was suggested? --2A02:AA1:102F:1E59:1443:C1AF:253E:994C (talk) 13:50, 14 November 2021 (UTC)
 * See Catalan's conjecture. D.Lazard (talk) 14:12, 14 November 2021 (UTC)
 * True, but my intended suggestion was suggested elsewhere on another article's talk page. --2A02:AA1:102F:1E59:B4CA:F078:2512:9431 (talk) 16:20, 14 November 2021 (UTC)
 * I found it, it was on reference desk topic mathematics. --2A02:AA1:102F:1E59:B4CA:F078:2512:9431 (talk) 16:24, 14 November 2021 (UTC)
 * It was at the math reference desk. The thread is here. ev iolite   (talk)  16:25, 14 November 2021 (UTC)

Math-heavy AfC draft
Hello mathematicians! I've been reviewing some old (>2 months in the queue) AfC drafts, and I ran into Draft:Geometric_rigidity. I don't have the background to actually see if what they are saying is totally fake or if it's based on reliable sources. Are there any AfC reviewers here who would be willing to take a look? I'm hoping to cut down the AfC backlog substantially over the next week or two. — Mikehawk10 (talk) 06:07, 12 November 2021 (UTC)
 * It's a real thing related to structural rigidity, although the first half of that draft definitely needs more referencing. Both Draft:Geometric rigidity and Draft:Structural rigidity (pinging who commented on the latter draft) were created by, based on this graduate course + this graduate course and the not-yet-published book based on their notes. Both drafts need to be written less technically, with WP:NOTTEXTBOOK in mind.If these drafts are ever published, the title of Geometric rigidity probably needs to be disambiguated with the widely-used concept of rigid analytic spaces (where rigid geometry points) from an entirely different area of mathematics. — MarkH21talk 06:21, 12 November 2021 (UTC)
 * OK. I'm don't follow the second paragraph's jargon, but what I'm hearing is that you believe that it's insufficiently sourced as-is to pass AfC, that the article is too jargony to pass AfC, and that some of the sources are unpublished. And, if the draft were accepted, I'd need to make a dab page when I accept it. Am I correct? — Mikehawk10 (talk) 06:25, 12 November 2021 (UTC)
 * Sorry, I just realized that I missed some of the references in the first few sections of Draft:Geometric rigidity from the "For more information, see [1]" type statements at the beginning of the level-1 headers (which shouldn't be used per MOS:HEAD). The referencing is actually largely okay. The draft probably just needs some copy-editing for minor MOS issues and a less technical introduction to pass, if not for the next issue.A bigger issue that I just noticed with the draft is that it refers to the definitions from Draft:Geometric constraint system, which is not in article space (it also needs a less technical introduction and some minor MOS cleanup). Regarding the titling, using Geometric rigidity (combinatorics) and/or creating a DAB page could work. Adding a hatnote using for or about is also an option. At least for the rigid geometry redirect right now, Rigid analytic space is definitely the WP:PRIMARYTOPIC based on a cursory Google Scholar search. — MarkH21talk 06:35, 12 November 2021 (UTC)
 * As well as rigid analytic space noted above, "geometric rigidity" needs disambiguation from Mostow rigidity theorem, at least, and maybe some of the other entries in Rigidity (mathematics). Anyway, my same comments as about the other draft apply: It is too technical, and it has too much overlap with structural rigidity to work well as a separate article. Also, I don't think the geometric rigidity draft's distinction that "structural rigidity" should only be about the generic case is accurate. But maybe some of the material from the draft could be used to expand structural rigidity, which could use some expansion. —David Eppstein (talk) 08:00, 12 November 2021 (UTC)
 * Appreciate the feedback about these drafts. The important developments in this established subarea of geometric constraint systems (namely combinatorial and geometric rigidity and related algebraic matroids), specifically definitions, examples, theorems, algorithms, applications are either mostly not available or weirdly unbalanced in the previously available articles on structural rigidity, rigidity matroid, dense graphs etc.Meera Sitharam (talk) 15:44, 12 November 2021 (UTC)Meera Sitharam
 * Adding to that: The pages were developed, based on this diagram Draft talk: Geiringer-Laman theorem intended as a service to the community. They were developed by graduate students - novices to wikipedia posting - in several courses that were taught at 2 institutions. There is no intention to advertise etc. I am not sure what unpublished book is being referred to in the discussion above, there is no book planned, just the usual lecture notes published in a course webpage. There is a 2018 published book Handbook of Geometric Constraint Systems which contains a lot of the material. I understand the constructive feedback as being of 3 types: "too technical" "disambiguate from existing pages" and "merge with existing pages." If you could help us by drilling down a bit further, it will help us make the changes effectively Meera Sitharam (talk) 15:58, 12 November 2021 (UTC)Meera Sitharam

I've accepted the draft, so please edit it, merge it, trim it, as you will. AfC was introduced to stop vandalism and hoaxes, and was never intended to be a high bar to creation by good faith editors. &mdash; Martin (MSGJ · talk) 22:04, 14 November 2021 (UTC)

LaTeX not showing up in table of contents for section header
The page Kähler–Einstein metric has developed the problem that some LaTeX code in section headers has stopped rendering properly in the table of contents. It renders fine in the actual header and this appears to be a new phenomenon (since it used to render fine in the table of contents also). Obviously it could be fixed by changing that to HTML math code instead although I thought this may be a rendering issue that appears elsewhere in case people hadn't noticed it.Tazerenix (talk) 15:31, 14 November 2021 (UTC)
 * I saw a similar issue in article Ordinal collapsing function. For blackboard bold, using HTML is deprecated, so for example I've seen "the $$\mathbb{C}^n$$ space" avoid the problem by changing the title to "the complex coordinate space". But using the extension:math I think it's difficult to link to a section. --SilverMatsu (talk) 00:24, 15 November 2021 (UTC)
 * MOS:FORMULA says explicitly that LaTeX markup must not be used in section headings. D.Lazard (talk) 10:29, 15 November 2021 (UTC)
 * The current bug is T295091. PrimeHunter (talk) 11:48, 15 November 2021 (UTC)
 * Thanks, I changed it to HTML.Tazerenix (talk) 12:29, 15 November 2021 (UTC)

Duodecimal -> Dozenal system?
I'm pretty sure duodecimal should not have been moved to dozenal system (the former is far more common outside of possible niche groups), but I can't undo it. XOR&#39;easter (talk) 14:05, 16 November 2021 (UTC)
 * Oy vey. --JBL (talk) 14:16, 16 November 2021 (UTC)
 * It seems I was able to reverse it. --JBL (talk) 14:18, 16 November 2021 (UTC)
 * Thanks. XOR&#39;easter (talk) 16:13, 16 November 2021 (UTC)

User:XǝNoX

 * Most of this editor's other edits are also terrible. Does anyone recognize the pattern?  It seems to me like probably a returning blocked user (based on the varied details of their bad edits). --JBL (talk) 14:25, 16 November 2021 (UTC)
 * - Including *exactly* 10 edits prior to the move *and* adding a user page and a talk page so those don't show up in red when looking at contributions *and* understanding how to do default sorts. Oh yeah, I'm watching this user. (Not sure I'll be able to do much)Naraht (talk) 14:43, 16 November 2021 (UTC)
 * For what it's worth, the user has edited frwiki so it makes sense that they would understand some of that. ev iolite   (talk)  14:47, 16 November 2021 (UTC)
 * And they've done the same move on the French wiki! Looks like they must be some fanatic of dozenal to me. NadVolum (talk) 17:29, 16 November 2021 (UTC)

Numerology
Anyone feel like taking a whack at improving the article on Numerology? I removed a lot of "in-universe" material that had accumulated, but it could be built up with serious perspectives from the outside (compare pseudomathematics). XOR&#39;easter (talk) 01:01, 17 November 2021 (UTC)

Poisson distribution
A number of newly-registered editors and IP editors have been having a week-long edit war about the PMF for Poisson distribution. Could we get a few more eyes on this article, and perhaps someone to give it a quick review to ensure everything is correct. Thanks. Mind matrix  02:54, 17 November 2021 (UTC)

Mathetimatics
What are equation with fraction 105.112.26.84 (talk) 20:35, 17 November 2021 (UTC)
 * "Equation with fraction" is a phrase that has no common definition, and is thus nonsensical without context. D.Lazard (talk) 21:13, 17 November 2021 (UTC)

Requested peer review of constant-recursive sequence
I have requested a peer review of constant-recursive sequence to try to broadly improve the article and solicit feedback from experienced Wiki editors. Caleb Stanford (talk) 22:33, 18 November 2021 (UTC)
 * In the thread above, it was a consensus for a merge. I have answered on the peer-review page that the merge must be done before the peer review. D.Lazard (talk) 23:14, 18 November 2021 (UTC)

Approximate inequality
WP:NOR concerns and thoughts about proper organization have been raised; see Talk:Approximate inequality. XOR&#39;easter (talk) 03:19, 21 November 2021 (UTC)
 * May be it's the Big O notation　? --SilverMatsu (talk) 03:43, 21 November 2021 (UTC)
 * I agree that this page should be deleted and reincorporated with wherever it came from. PatrickR2 (talk) 05:34, 21 November 2021 (UTC)
 * I agree the title should be changed, but I don't think the page should be deleted: the symbol ≪ is used in both formal and informal contexts and we should have an article which explains the usage of the symbol. I don't think "approximate inequality" is the right name for it though. Caleb Stanford (talk) 16:32, 21 November 2021 (UTC)
 * I think the word "approximate inequality" is probably appropriate for ⪅ (no idea in what context that is used), for ≪ the correct reading is "much less than". Caleb Stanford (talk) 16:33, 21 November 2021 (UTC)
 * has over 40000 edits and should be able to do better. This is a conflation of ⪅ (approximately less than) and ≪ (much less than) at a title that implies there is no conflation.  It should probably just be merged back to Inequality, as there is little to say beyond the definitions and Unicode points. User:力 (powera,  π,  ν ) 16:36, 21 November 2021 (UTC)
 * Before 's edits, the paragraph on ≪ in Inequality (mathematics) was correct, although not sourced. I suggest to restore it.
 * For ⪅ (approximately less than), I have no idea about a possible mathematical meaning, and I do not know any example of use (no source is provided). So, there is no reason for mentioning this symbol in mathematical articles. I strongly support the deletion of the new article approximate inequality, and the redirect of ⪅ to the right table of Unicode symbols. D.Lazard (talk) 17:15, 21 November 2021 (UTC)
 * I hadn't realized that this was split off just two days ago. I have reverted the (poorly conceived) removal of content from the article Inequality (mathematics).  I agree with D.Lazard about the right course of action for Approximate inequality. --JBL (talk) 18:39, 21 November 2021 (UTC)
 * I'm afraid folks have no idea about ≈ (approximately equal to) either? $$a \approx b: |a-b|<\epsilon$$ fgnievinski (talk) 01:14, 22 November 2021 (UTC)
 * Approximate inequality is used in geometric measure theory as a synonym for a reasonably tight bound, for example in concentration inequalities, . It might be worth a mention in concentration inequality, but is probably not independently notable. -- 17:18, 21 November 2021 (UTC)
 * I've reverted all the "much less than" and "much greater than" redirects to point to Inequality (mathematics) again. I'm less convinced than some of you that "approximate inequality" can't be an article, so I'll leave those symbols for further discussion. User:力 (powera,  π,  ν ) 18:58, 21 November 2021 (UTC)
 * If there is uncertainty about the relative values of x and y, then x is approximately equal to or less than y is the same as saying NOT ( x is necessarily greater than y ). This could be mistaken for NOT ( x is much greater than y ) which may explain the odd combination of the two in one article. JRSpriggs (talk) 19:37, 21 November 2021 (UTC)

Article is now at AfD. --JBL (talk) 21:16, 21 November 2021 (UTC)

Math-format-disimprovement gnome
The IP gnome who adds \left \right to all the parens (making them bigger than needed for inline text and causing Wikimedia's dubious-quality math formatting to become even lower-quality by introducing extra spacing around the parens) is back: see Special:Contributions/109.70.40.55. —David Eppstein (talk) 01:28, 22 November 2021 (UTC)
 * They have an annoying BKFIP-like tendency to mix trash and good edits together (as well as a similar temperament when reverted). --JBL (talk) 12:11, 22 November 2021 (UTC)

New LTA casefile
I've made a new long-term abuse casefile for, a sockpuppeteer from Taiwan who has added large quantities of fancruft and OR at mostly integer-related articles since August 2018. You can review and refine the casefile at Long-term abuse/Xayahrainie43. –LaundryPizza<b style="color:#b00">03</b> ( d c̄ ) 08:21, 22 November 2021 (UTC)
 * Thanks, it looks like a very clear summary. --JBL (talk) 12:31, 22 November 2021 (UTC)

Subclass reachability
Hello, I found this little stub while trawling orphaned articles. Should be remain a standalone, or would it be better off merged into a larger topic? &spades;PMC&spades; (talk) 02:33, 18 November 2021 (UTC)
 * The article is inactive since 2015. It contains of just one sentence, and no sources. If it is of any use in a larger article on a broader subject, it is easy to insert there a similar sentence "from scratch". (In the worst case, the notion is just a local definition in some machine learning journal article; a machine learning expert might comment on that.) For these reasons, I'd be in favor of deleting the article. - Jochen Burghardt (talk) 09:50, 18 November 2021 (UTC)


 * The main article on Computational learning theory does not ever use the word "reachable" and I also haven't heard of this terminology. I would also therefore vote delete. Caleb Stanford (talk) 22:30, 18 November 2021 (UTC)
 * Tagged for PROD, thanks guys. &spades;PMC&spades; (talk) 22:51, 18 November 2021 (UTC)
 * and, the article was de-PROD'd today with the edit summary "Merge to reachability problem is a better option in this case per WP:ATD". Do you guys think that would be suitable, or do you still feel it's more likely to be a neologism/limited-use term? &spades;PMC&spades; (talk) 00:03, 23 November 2021 (UTC)

About some templates that use blackboard bold
MOS:BBB recommends not to use Unicode for blackboard bold. Can I change the template image in the list from Unicode to Extension:Math ? --SilverMatsu (talk) 03:26, 20 November 2021 (UTC)

list

 * Template:Algebraic numbers
 * Template:Real numbers
 * Template:Complex numbers
 * Template:Rational numbers (This seems okay, but I added it to the list because the filename is Unicode)
 * I don't see the point of having the decorative BBB image there at all. Also the algebraic number navbar includes a unicode Q in the list of links as well, again I think unnecessarily. Also also while we're discussing this it would be helpful if Ring theory sidebar had a navbar version so it could be used more unobtrusively. —David Eppstein (talk) 08:11, 20 November 2021 (UTC)
 * Thank you your reply. I removed BBB image. --SilverMatsu (talk) 04:13, 23 November 2021 (UTC)

Notification
Galileo Galilei has been nominated for a community good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. Jo-Jo Eumerus (talk) 15:51, 25 November 2021 (UTC)

Vandalism of "Limit inferior and limit superior"
The article Limit inferior and limit superior is being periodically vandalized by the same unregistered user (appearing as a changing ip address only). From the history page, this started on 22 Sep 2020 (possibly earlier) and occurred on at least 8 occasions, the last one today, the offending editor adding a nonsensical sentence usually at the same spot, often related to Denmark (as also indicated in contributions by one of the IP addresses). After someone removes the spam, he usually waits a week and puts it back in. I am not really familiar with the way administrators handle this type of things. Any suggestions on how to handle this? PatrickR2 (talk) 02:40, 26 November 2021 (UTC)


 * I've submitted a request to WP:RFPP (requests for page protection) here, asking for pending changes protection, which will let autoconfirmed users edit normally but require IPs' and new users' edits to be approved first; an admin will soon look over and enact it if they believe it to be warranted. Thanks, ev iolite   (talk)  03:44, 26 November 2021 (UTC)


 * Thanks, PatrickR2 (talk) 05:16, 26 November 2021 (UTC)

about Holomorphic separability
I suggested changing the title of the article. See Talk:Holomorphic separability. thanks! --SilverMatsu (talk) 13:47, 26 November 2021 (UTC)

Pge title for trigonometric numbers
Hi, I think the conversation here could benefit from a fresh pair of eyes. The main question (I think) is what the page title should be for the content that's currently at trigonometric number, which was recently sort of selectively merged from trigonometric constants expressed in real radicals. Danstronger (talk) 04:00, 27 November 2021 (UTC)
 * I have suggested Algebraic trigonometric value, which describes well the content of the article, that is, algebraic expressions for the algebraic values of trigonometric functions. D.Lazard (talk) 11:27, 27 November 2021 (UTC)

Symlet
I found this unsourced two−line stub, very likely not independently notable. Is it worth merging somewhere, maybe to Daubechies wavelet? Lennart97 (talk) 19:16, 26 November 2021 (UTC)
 * Google Scholar finds 69 sources for intitle:symlet, and MathSciNet (more focused on good-quality sources, but also likely missing some of the good quality ones in engineering rather than mathematical publications) finds 7 for anywhere:symlet, including the textbook source Wavelet packets and their statistical applications . I think there is probably enough sourcing to expand this stub rather than to merge it. —David Eppstein (talk) 20:24, 26 November 2021 (UTC)
 * Thanks David. In that case, anyone interested in expanding this article? :) Lennart97 (talk) 12:13, 27 November 2021 (UTC)

Difference equation
I have just created the redirect that appeared as a red link in almost 150 articles. The target of the redirect is Finite difference, to which I have added a definition of a difference equation in the lead ("difference equation" were already bolded in the lead, but without a definition).

The result is not fully satisfactory, as the finite difference operator and difference equations appear in many areas of mathematics, and particularly in combinatorics, while the target article is essentially devoted to the use in numerical analysis. So, some more work is needed, that I am unwilling/unable to do myself. D.Lazard (talk) 10:05, 29 November 2021 (UTC)
 * In fact, difference equations and recurrence relations are equivalent concepts, in the sense that they define exactly the same sequences. I did know that, but I forgot it because of the confuse section . I'll rename and rewrite this section, then redirect there.