Wikipedia talk:WikiProject Mathematics

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Integer factorization

The article integer factorization lists a lot of algorithms. I think it should say what algorithms are the most practical. Somewhere (I couldn't find it again) I read that Shanks's SQUFOF is clearly the best for $n<2^{64}$, or something a little bigger than that; that Quadratic Sieve was best for some range, and that something else was better for some other range.

Can someone add that to the article? Bubba73 ^{You talkin' to me?} 17:54, 30 October 2023 (UTC)

And General number field sieve says that it is best for integers over 100 digits. So what are the approximate range where each is the best? Bubba73 ^{You talkin' to me?} 05:06, 1 November 2023 (UTC)

Also, I think it would be good to have an article about how to factor an integer. I remember a journal article with that title decades ago. Also, Knuth, volume 2, § 4.5.4 goes through a process, but it is out of date. He first does trial factorization and then switches to Fermat's method, which isn't currently the best thing to do. Bubba73 ^{You talkin' to me?} 01:06, 5 November 2023 (UTC)

What are the approximate range where each is the best? This strongly depends on the used computer architecture and the used basic algorithms (integer multiplication, linear algebra, ...). So, I doubt that any reliable encyclopedic answer can be provided.

I think it would be good to have an article about how to factor an integer. See WP:NOTHOWTO. D.Lazard (talk) 11:35, 5 November 2023 (UTC)

More accessible explanations near the front, some historical discussion, possibly an example or two, and some explicit comparison of various methods wouldn't necessarily make integer factorization into a "howto". What we have now is mostly a list of wikilinks to various methods with no explanation or context. A novice reader of the integer factorization page (say a high school student) isn't going to get much out of it, even if integer factorization is relevant to one of their interests or projects, because the page is written in a pretty inaccessible way.

But Bubba73, what did you have in mind? You can always try adding the information you are looking for to the article. Or if you propose something concrete maybe others can help. –jacobolus (t) 14:46, 5 November 2023 (UTC)

I would want some reference on which to base such an article. Something like try trial division up to some point, and if that fails to completely factor it, do a primality test on what remains. If it is composite, then try to factor it with method X. etc. Bubba73 ^{You talkin' to me?} 22:15, 5 November 2023 (UTC)

The Joy of Factoring, by Wagstaff, page 247 gives several tips. It also says that the Quadratic Sieve is best for numbers with 50-100 digits and the Number Field Sieve is best for numbers with more than 100 digits. At least that should go in the integer factorization article. Bubba73 ^{You talkin' to me?} 22:30, 5 November 2023 (UTC)

Is that ten-year-old comparison still accurate, though? As of a different 2011 comparison the crossover was more like in the low 90s [1] and since then some NSF implementations have had significant speedups [2]. Later posts in the same thread put the crossover at around 100 again. —David Eppstein (talk) 23:18, 5 November 2023 (UTC)

Probably not. I'm not up to date on this. But it may give a rough idea. It could be in there with the date of the statement, and note that things change, and it depends on other factors. Bubba73 ^{You talkin' to me?} 00:48, 6 November 2023 (UTC)

I tried to make the first paragraph of integer factorization a bit more accessible. I think it would still be good to add another paragraph to the lead (and another section to the article) describing pre-computer pen-and-paper factorization algorithms and efforts. –jacobolus (t) 23:47, 5 November 2023 (UTC)

Regarding "how to", it shouldn't have the name "how to factor an integer", but something like "method to factor an integer". Also, greatest common divisor tells you "how to" find the GCD. Bubba73 ^{You talkin' to me?} 03:09, 21 November 2023 (UTC)

"factoring algorithms" —Tamfang (talk) 05:39, 25 November 2023 (UTC)

That's the right idea, but the more idiomatic phrase (maybe 2.5x more popular in Google Scholar) is "factorization algorithm" (singular because that's what Wikipedia tends to do). —David Eppstein (talk) 08:04, 25 November 2023 (UTC)

Something like that, but not just a list of factoring algorithms, but something to give guidelines about what should be used and when. I don't have a reference for this, but, unless you know that there are no small factors, I always start with some trial division. Sometimes trial division is enough. But after a certain number of small factors have been checked, do a primality test on what remains. (And you may want to do a primality test right after some factors have been found.) If it is composite, then what you do next depends on how large the remaining number is. Bubba73 ^{You talkin' to me?} 21:53, 25 November 2023 (UTC)

Summarizing Wagstaff's tips:

1. Do at least a probable prime test first

2. Look for small factors

3. Trial division first, then ECM with a small bound and increase the bound, if necessary

4. Parallelize if you can

5. Remember that Pollard Rho and ECM may not find factors in order

6. Choose the best algorithm for the size of the number. Quadratic Sieve is fastest for 50-100 digits and Number Field Sieve is fastest for more than 100 digits.

7. when a factor is discovered, check it for primality. Use the BPSW test. If you need to prove a number to be prime, use the Elliptic Curve Prime Proving method, or if you can factor p-1, use one of those methods.

Now, this isn't what I do because I always check for some small factors before a primality test, etc. Bubba73 ^{You talkin' to me?} 22:22, 25 November 2023 (UTC)

Disambiguation of Two-dimensional space

Could you help to disambiguate links to Two-dimensional space? There are a lot of articles (shown in this list which link to the dab page. Not all would fall under this wikiproject but many are either related to Surface (mathematics) or Plane (mathematics) and I don't have the expertise to know which.— Rod ^talk 21:45, 26 November 2023 (UTC)

At a glance, this looks like a merge opportunity? I don't see why surface (mathematics) and surface (topology) shouldn't be a single article, particular when the "mathematics" one is glossed in the disambig page as "a topological space of dimension two". Planes are more specific than 2D spaces and probably should not be in the mix here at all. --Trovatore (talk) 22:42, 26 November 2023 (UTC)

I agree that merging surface (mathematics) and surface (topology) is probably a good idea, but I don't think that planes should be excluded from the disambiguation of 2D spaces. If someone is searching for 2D spaces, they'd probably expect planes to show up as a prominent and canonical example. --MtPenguinMonster (talk) 08:45, 27 November 2023 (UTC)

I don't think these should necessarily be merged. There's plenty to say separately about topological vs. other kinds of features. If we want a merge target for a top-level article about surfaces, it should probably be a merger to surface, which is currently very mediocre. Someone who knows/cares about surfaces in a reasonably wide range of contexts should try to think carefully about how various topics related to surfaces should be be organized into multiple articles, and then split those topics between a few articles with clearly defined scope, which can all be linked from surface as an overview article. –jacobolus (t) 10:47, 27 November 2023 (UTC)

Surface is already an overview article, it reached its current form after a lot of debate with physics and computing editors. It'd be the worst place for merging Surface (topology) -- non-mathematicians are not so excited about topology, sorry. In fact, Surface (geometry) could well be split from Surface (mathematics), as there's a lot to be said about mathematical surfaces to a general audience without mentioning, gosh, "manifolds". Unfortunately, elementary geometry concepts in general don't seem to attract as much attention from math editors at Wikipedia. fgnievinski (talk) 02:52, 6 December 2023 (UTC)

I think this should redirect to Plane (mathematics), which (perhaps along with Euclidean plane or Coordinate plane) is the intended target for the vast majority of inbound links, and which could also discuss general surfaces in a section. @Fgnievinski recently switched from that to a disambiguation page in special:diff/1183701575 without any discussion or consensus, and I think it was a significant mistake. –jacobolus (t) 10:38, 27 November 2023 (UTC)

I reverted to the version which is a redirect. If there is going to be a disambiguation page, it should be under a title like two-dimensional space (disambiguation), with two-dimensional space redirecting to plane (mathematics) which is the commonly intended target. –jacobolus (t) 10:54, 27 November 2023 (UTC)

Surely somebody looking for information on, e.g., ellipsoids, would find a redirect to plane to be perverse. Certainly spheres is a commonly intended target. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:55, 27 November 2023 (UTC)

Why would someone wanting to direct readers to ellipsoids put a wiki-link to two-dimensional space? In my opinion that would be ridiculous, and it seems vanishingly unlikely. –jacobolus (t) 12:59, 27 November 2023 (UTC)

The same question applies to planes; why would someone wanting to direct readers to planes put a wiki-link to two-dimensional space? That seems just as ridiculous and unlikely. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:22, 27 November 2023 (UTC)

In my mind the words "line", "plane", "space" are shorter synonyms for "1-space", "2-space", "3-space" (which originally arose in a context where "space" always meant 3-space).

What do you take 2-space to mean? –jacobolus (t) 18:13, 27 November 2023 (UTC)

I think "plane" by default means Euclidean plane, whereas 2D space definitely does not imply Euclidean, basically ever. I not only don't think "plane" is a reasonable redirect target, I don't even think it should be linked from this target. I think surface (mathematics) and surface (topology) should be merged, and two-dimensional space should redirect to the merged article. Or possibly the merged article should just be named "two-dimensional space". --Trovatore (talk) 18:28, 27 November 2023 (UTC)

I agree with jacobolus. Here are the first few links to two-dimensional space grabbed from https://en.wikipedia.org/wiki/Special:WhatLinksHere/Two-dimensional_space:

• Cartesian coordinate system is about planes
• Real coordinate space is about planes
• Gas electron multiplier maybe shouldn't be linked to any of these articles but if it should then it should be about planes
• many of them (like Piranha 3D, XLfit, Photo psychology, and List of Aqua Teen Hunger Force characters) shouldn't be linked to any mathematical article, but certainly should not be linked to articles about topological surfaces
• Plane of rotation is about planes

Maybe somewhere in Wikipedia someone has linked two-dimensional space when they should have linked something about surfaces, but mostly people are trying to link to something specifically about planes (possibly not in a truly mathematical sense). --JBL (talk) 18:44, 27 November 2023 (UTC)

"Plane" means a wide variety of different things depending on the context, and in my impression is a precise and almost completely interchangeable synonym for "two-dimensional space". For example "hyperbolic plane" = "two-dimensional Riemannian space of constant negative curvature" and "projective plane" = "two-dimensional projective space". Without qualification or context both of these most often mean a Euclidean plane (flat 2-space with a concept of distance), but sometimes mean an affine plane or some other kind of plane. (One slight difference in common use I have observed is that often "two-dimensional space" is used to mean the whole context for the geometry, while "plane" is often used for, more specifically, a "two-dimensional subspace".) –jacobolus (t) 18:57, 27 November 2023 (UTC)

Comment Without any comment on the substance of the matter, I would just like to point out that the intended targets of the links to the page will be heavily biased towards planes simply because that is where the term lead until recently. So anyone who would have wanted to link anywhere else may well have considered linking to Two-dimensional space and then seen that the target is not where they intended to point. Felix QW (talk) 19:49, 27 November 2023 (UTC)

Yes, I think most of these links to "two-dimensional space" just need to be fixed at the link.

Jacobulus points out that "plane" doesn't always mean "flat plane", but I think it does by default, whereas "two-dimensional space" does not mean flat by default.

Maybe stickier, what about $S^{2}$? That's a two-dimensional space, but I think is very unlikely ever to be called a "plane".

I think basically any link to "two-dimensional space" where the reader would be surprised to arrive at an article that includes $S^{2}$ — is just an incorrect link and should be fixed in the text of that article. --Trovatore (talk) 23:57, 27 November 2023 (UTC)

Both of these imply flat when left unqualified. Cases where someone wants a curved space are either called "surface" or e.g. "curved two-dimensional space". But anyway, the 2-sphere is definitely a type of "plane" just like the hyperbolic plane or elliptic plane (historically the sphere was occasionally called the "Riemannian plane" (example 1, example 2), especially when someone wanted to emphasize an intrinsic/axiomatic definition, but that's somewhat ambiguous and now I think usually means something else). It's typically called the "sphere" rather than any kind of "plane" primarily because the concept of a sphere is ~2000 years older than the concept of a "curved plane", but perhaps also because "elliptic plane" is used to mean the sphere with antipodal points identified. Confusingly, the ancient Greek term "line" means any curve and the flat version was explicitly called a "straight line", which is sort of the opposite situation from what we deal with in the 2-dimensional case; in French they picked a better abbreviation and call straight lines "straights" for short. All of these various inconsistencies and ambiguities in nomenclature came about because these names were established long long before they were generalized, and then the generalization was done piecemeal and incoherently by a variety of different authors and translators. –jacobolus (t) 02:47, 28 November 2023 (UTC)

I'm not sure what you mean by "both of these". The phrase "two-dimensional space" absolutely does not imply flat when left unqualified. --Trovatore (talk) 07:16, 28 November 2023 (UTC)

Yesterday I spent 20 minutes skimming through academic papers matching the search result "two-dimensional space", and when unqualified this is usually referring to the Euclidean plane. Examples include children learning about maps, computer algorithms for segmenting images, wallaper groups, modeling car traffic, surfaces projected onto their tangent space, fractals, graph algorithms for graphs embedded in the plane, imaging of thin slices of some three-dimensional material, etc. There are also lots of papers talking about "curved two-dimensional space", "two-dimensional space-time", "non-Euclidean two-dimensional space", etc., but even these are not too often used for just any old surface from what I can see. Examples where there is an arbitrary surface include e.g. robot kinematics where there's some "two-dimensional space" of available motion for some part, and computer graphics mapping an image parametrically onto a triangle mesh; these are examples of real coordinate space. –jacobolus (t) 15:13, 28 November 2023 (UTC)

I'm really having trouble seeing why you would ever not want to just say "plane" if you mean a flat 2D space. "Plane" very clearly says it's flat (a plane is a tool used to make things flat). "Two-dimensional", on the other hand, says nothing whatsoever about flatness, just about the number of independent ways you can move in the space. --Trovatore (talk) 17:15, 28 November 2023 (UTC)

What this demonstrates is that you've absorbed a particular expert perspective so far as to lose sight of how non-experts use words and language, rather than anything about the encyclopedia. The usage of "two-dimensional" to mean "planar" is common, widespread, and rarely causes confusion. (By contrast, the usage of "two-dimesional" to describe a curved surface embedded in three-space causes lots of confusion.) --JBL (talk) 17:46, 28 November 2023 (UTC)

I'm not trying to psychoanalyze anyone; I'm just telling you that in practice "plane" and "two-dimensional space" are typically treated as synonyms. But as I suggested below, I think we could make an article at two-dimensional space. The tricky part then is figuring out how to organize (and ideally expand) material between there, plane (mathematics), Euclidean plane, inversive plane, hyperbolic plane, sphere, affine plane, projective plane, coordinate plane, surface, surface (mathematics), surface (topology), etc., most of which are currently mediocre. The part I think is a bad idea is encouraging meat-bots to go "fix" every wikilink pointed at two-dimensional space so they don't land on a disambiguation page, which is apparently banned. –jacobolus (t) 17:47, 28 November 2023 (UTC)

Maybe it's useful to consider a different approach to the problem: under what circumstances would someone put a link to two-dimensional space? Are there scenarios where someone would be more likely to link to two-dimensional space than to an article like plane or surface? --MtPenguinMonster (talk) 09:08, 28 November 2023 (UTC)

One other possibility would be to make a short halfway-to-disambiguation page modeled on one-dimensional space. –jacobolus (t) 19:11, 27 November 2023 (UTC)

The only thing certain after this lengthy debate is "Two-dimensional space" is an ambiguous term. It's only natural, then, to make it a disambiguation page. It could be marked with {{bca}} if there's hope to write something unique about it. But please avoid duplicating Plane (mathematics) and Surface (mathematics) (or Surface (topology)). fgnievinski (talk) 03:13, 6 December 2023 (UTC)

No it should absolutely not be a disambiguation page. –jacobolus (t) 03:36, 6 December 2023 (UTC)

We should abide by the WP:DAB policy -- there's no WP:PRIMARYTOPIC, hence the dab page. BTW: your reasoning is inconsistency with the explanation in Dimension, esp. the analogy with degrees of freedom. fgnievinski (talk) 03:41, 6 December 2023 (UTC)

(Note: I've formalized this redirect discussion at Wikipedia:Redirects_for_discussion/Log/2023_December_6#Two-dimensional_space. fgnievinski (talk) 03:46, 6 December 2023 (UTC))

We should abide by the fundamental and abiding policies of "do what's best for readers" and "do what makes the best encyclopedia". But since you really seem to like WP:THISANDTHAT abbreviations, take a look at WP:CONCEPTDAB.

your reasoning is inconsistent – you are going to have to elaborate. I don't understand what you are getting at. –jacobolus (t) 03:43, 6 December 2023 (UTC)

If you'd like to write a "short halfway-to-disambiguation page modeled on one-dimensional space" that's fine. I'm curious what could be said about two-dimensional space beyond what's already stated in Plane or Surface. But since that broad-concept article (BCA) doesn't exist yet, I had proposed to mark Two-dimensional space (disambiguation) with the {{bca}} template. That can be done whether or not Two-dimensional space redirects to the DAB page or to an existing article.

I claim there's an inconsistency in holding "in practice 'plane' and 'two-dimensional space' are typically treated as synonyms" then explaining Dimension as "the number of degrees of freedom of a point that moves". If Wikipedia defines two-dimensional space as not necessarily flat, then it should redirect consistently, hence to Surface (mathematics).

If you insist on the typical notion, 2D=planar, then Two-dimensional space should redirect to Euclidean plane, the one most closely corresponding to the physical, geometrical or everyday notion. This is analogous to Three-dimensional space and Euclidean 3-space already being covered in the same article.

Finally, since everyone here seems to have a different opinion, the DAB page would be a compromise solution. At least until a BCA emerges. fgnievinski (talk) 04:35, 7 December 2023 (UTC)

No, a disambiguation page is not a compromise; a disambiguation page is a significant disruption that forces a broad swath of other pages to immediately change, because a different [in my opinion misguided/too rigidly applied] policy holds that wiki-links can't point at disambiguation pages, and there are scripts for hunting such links and editors who feel an urgent need to go "fix" them right away causing a wave of unnecessary edits. (This policy is helpful in the typical case, e.g. an inbound link to Amazon should almost certainly be either the mythical tribe, the river, or the company, and pointing at a disambiguation page is going to be confusing to readers.) A quick fix is a redirect + hatnote, and a higher-effort solution is some "broad concept article".

Even though Euclidean plane was originally titled two-dimensional space, then later moved (by you) to Two-dimensional Euclidean space, and finally moved (by me) to Euclidean plane, and even though the most common meaning of "two-dimensional space" in the literature is the Euclidean plane, I don't think two-dimensional space should be a redirect to Euclidean plane, because the term itself is much broader / less specified, and does not (per se) imply the Euclidean plane. References in physics literature to "two-dimensional space" with constant curvature (sphere or hyperbolic plane) are pretty common. Other references to "two-dimensional space" mean the affine plane or the real coordinate space of 2 dimensions.

In my opinion all of the articles related to planes and surfaces (plane (mathematics), Euclidean plane, inversive plane, hyperbolic plane, sphere, affine plane, projective plane, coordinate plane, complex plane, surface, surface (mathematics), surface (topology), etc., with the notable exception of differential geometry of surfaces) are mediocre, substantially incomplete, and somewhat neglected, and would benefit from significant additional work searching for sources, synthesizing them, writing clear explanations, drawing attractive figures, etc. (If anyone wants to make a bigger collaboration about this, it would be a good general project.) –jacobolus (t) 05:28, 7 December 2023 (UTC)

Indeed there is a lot to be improved. On the topic of two-dimensional spaces: where do we cover general two-dimensional vector spaces? While they are of course isomorphic to the Euclidean plane, some natural examples like the solution set of a second order homogeneous linear ODE do not look like a plane to the learner. —Kusma (talk) 06:48, 7 December 2023 (UTC)

I think "space" doesn't usually mean "vector space", unless there's been specific context established. I'm skeptical that there should be a whole article about two-dimensional vector spaces, but I guess it's not completely outlandish. But even if there were such an article, I don't think it would be in contention for the (or even a) primary meaning of "two-dimensional space". --Trovatore (talk) 17:44, 7 December 2023 (UTC)

That "space" has mathematical meanings beyond vector spaces is a relatively advanced concept. "Two-dimensional" is also a fairly advanced concept when you are not talking about vector spaces. —Kusma (talk) 20:03, 7 December 2023 (UTC)

So saying that a surface is two-dimensional is "a fairly advanced concept"? That is absurd. —Quondum 16:40, 8 December 2023 (UTC)

@Fgnievinski I started writing a (currently barely beyond stub level) draft article at user:jacobolus/2d. Even this one so far is better than a disambiguation page though, in my opinion. –jacobolus (t) 04:38, 8 December 2023 (UTC)

Thank you, that's pretty readable. Would it be possible to say something about the difference (or lack thereof) between plane and surface in non-Euclidean spaces? You alluded to above the usage sometimes is mostly historical. Or just sidestep the issue and say planes and surfaces are two-dimensional flat spaces and curved spaces, respectively? fgnievinski (talk) 06:08, 8 December 2023 (UTC)

I wonder if there's a good source about this. According to Wiktionary, the English words 'plane' and 'surface' come from Latin originally for 'flat' and 'top surface' (like a tabletop maybe?) respectively. I'm not exactly sure what the various relevant Ancient Greek words were.

In any event, in mathematics my impression is that the concept of a "plane" originally meant a flat (infinitely extensible?) surface, while a "surface" meant the boundary of some solid shape. (In English translations of Euclid's Elements, the definitions are that "a a surface is that which has length and breadth only", while "a plane surface is a surface which lies evenly with the straight lines on itself", analogous to the distinction between "line" and "straight line". Later things called "planes" were drawing on some analogy with the Euclidean plane, while later things called "surfaces" were drawing on some analogy with an arbitrary boundary of a solid shape, but from one to another it wasn't always the same analogy. I'm not sure there's really an entirely clean separation that can be made between them. But it's possible there are some sources that have tried. –jacobolus (t) 08:14, 8 December 2023 (UTC)

A good start, but

1. I don't believe that it is appropriate to mention planes in the first sentence, since not all 2-surfaces are planes.
2. The reference to parallel lines is confusing. The discussion should take into account that only on a flat space is a curve at a fixed distance from a given line guarantied to be a straight line. Also, on the hyperbolic plane the literature refers to lines as parallel that are not at a fixed distance from each other.
3. It wouldbe helpful to mention that some, but not all, surfaces are the boundaries of solids.
4. A double torus (sphere with two handles) is a simple example of a surface that is not a plane, and a mobious strip is a simple example of a surface that is not the boundary of a solid.

Is it TMI to mention that the use of coordinates might require multiple coordinate patches (charts)? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:21, 8 December 2023 (UTC)

The reason to mention planes at the start is that "two-dimensional space" as used in academic literature (which appears most plentifully in other applications rather than pure mathematics papers) most commonly means some kind of plane.

I think some kind of explanations about parallel lines is the clearest / most historically important / most common way of describing the difference between the sphere/plane/hyperbolic plane (vs. e.g. observations about the circumference vs. diameter of circles or the sum of internal angles of a triangle), but you're probably right there's some better phrasing. Maybe someone has seen a source with a good brief summary? It's hard to condense into 1–2 sentences.

It would be helpful to mention that some, but not all, surfaces are the boundaries of solids. This could certainly be mentioned, though I'd maybe put it in a later section. How often are the boundaries of arbitrary solids ever called "two-dimensional space"?

Is it TMI to mention that the use of coordinates might require multiple coordinate patches (charts)? To be honest I'd conceptually really rather say that a 2-dimensional space has points with two degrees of freedom (our current article there is a stub) or that a point can slide in two independent directions, rather than saying that points in 2-dimensional space can be represented by two coordinates; I just couldn't find a way to write that which was concise enough while being very legible/accessible.

There's obviously a great (great) deal that could be said here. For instance, a new section could be added unpacking each sentence or two of what I wrote so far. My main goal with this initial draft was to effectively disambiguate this article title so someone arriving there from a wikilink or search can find the more specific page they're looking for, which I don't think a traditional bullet list disambiguation page really accomplishes. –jacobolus (t) 18:51, 8 December 2023 (UTC)

The redirect of Two-dimensional space to Plane (mathematics) just seems awfully wrong to me. I think it should become the disambiguation page rather than having Two-dimensional space (disambiguation) as well. I agree 2D or even 2D space mostly means a plane - but two-dimensional space only includes the plane as one of many instances. 2D implies a specific instance, spelling it out means the general type of space. NadVolum (talk) 13:13, 7 December 2023 (UTC)

I also had a look at Google and it was not at all obvious to me what was the usual use of 'two-dimensional space'. The usual one of a space with two parameters seemed very common. The flat meaning of plane was not as common as implied above, the main place I saw it meaning a pane was in vectors and matrices where a subspace was mostly referred to instead. NadVolum (talk) 13:25, 7 December 2023 (UTC)

Disambiguation of other terms

Thanks for all the edits, reverts and discussion on this, with lots of useful ways forward. If anyone had any good ideas about links to the dab page Parametrization (shown at Disambig fix list for Parametrization that would be great as well.— Rod ^talk 15:31, 28 November 2023 (UTC)

And links to Tensor category (shown here) are also giving me grief trying to disambiguate them.— Rod ^talk 16:19, 28 November 2023 (UTC)

Isbell conjugacy, Isbell duality

I think Isbell conjugacy may be an another name or subsection of the (article of) Isbell duality (See also Codensity monad#Relation to Isbell duality). So, I think it might be possible to merge those two articles. Also, if articles are merged, which is better, Isbell conjugacy or Isbell duality ? SilverMatsu (talk) 16:33, 30 November 2023 (UTC)

What is the second article? Isbell duality is a redlink. - CRGreathouse (t | c) 17:21, 30 November 2023 (UTC)

Oops, I overlooked that it was a red link. --SilverMatsu (talk) 17:38, 3 December 2023 (UTC)

I am considering moving Isbell conjugacy to Isbell duality. In that case, Isbell conjugacy is a redirect to Isbell duality. --SilverMatsu (talk) 03:40, 5 December 2023 (UTC)

External (mathematics)

The article External (mathematics), describing a concept in abstract algebra, has been prodded basically for the reason that it is unsourced and appears to be original research. Is it? If not, maybe someone who knows more can rescue it by finding some sources and removing the prod. —David Eppstein (talk) 01:49, 5 December 2023 (UTC)

I would like to add that Internal operation seems to be a redirect to Operation (mathematics), and External operation seems to be a redirect to Binary operation. --SilverMatsu (talk) 04:47, 5 December 2023 (UTC)

And furthermore, the binary operation page that "external binary operation" redirects to has no mention of "external binary operation".

As already explained in Talk:External (mathematics) multiple times since 2011, this is original research and I agree it should be deleted. But I can't find the link to the place where we can support/oppose the deletion. Any idea? PatrickR2 (talk) 00:14, 6 December 2023 (UTC)

You could add a {{prod2}} to the article. Or you could just watchlist it to make sure it gets deleted rather than unprodded and then participate in the inevitable deletion discussion if it doesn't. —David Eppstein (talk) 02:05, 6 December 2023 (UTC)

Disambiguation of links to Range of a function

Could you help to disambiguate links to Range of a function. The list of articles shown at Disambig fix list for Range of a function include links to the dab page but it is often unclear which article the target should be. Any help appreciated.— Rod ^talk 08:19, 5 December 2023 (UTC)

The correct solution is almost certainly that the very recent deletion of the article at that location be reverted. --JBL (talk) 17:23, 5 December 2023 (UTC)

I reverted the change. It might be better to focus this article a bit on the history of the term 'range', since the concepts are already discussed at codomain and image (mathematics). –jacobolus (t) 17:34, 5 December 2023 (UTC)

Thanks. (My first thought was that I had fixed this a few years ago, but it turns out that what Tea2min and I fixed were links to Domain (mathematics) and Range (mathematics).) --JBL (talk) 18:23, 5 December 2023 (UTC)

@Rodw By the way, thanks for bringing these here instead of just trying to change all of the inbound wikilinks. In most situations where an article with a large number of existing inbound wikilinks is suddenly turned into a disambiguation page, it's at least worth having a conversation before trying to make mass changes, as often in such situations the disambiguation page is a controversial solution not backed by consensus. –jacobolus (t) 00:26, 6 December 2023 (UTC)

@Fgnievinski really wants this to be a disambiguation page. Maybe we can have a fuller discussion here. In my opinion the clearest for readers is to clearly describe at range of a function what the historical usage was of the term 'range'. Codomain and image are closely related concepts which in many contexts end up meaning the same thing, and there was historically a less stringent / less fully developed function concept, and various related terms were used in various looser or less precise (and sometimes a bit contradictory) ways. I think there should be an article (rather than disambiguation page or redirect) about the term "range", so that this can be clearly described. Then readers who encounter this term somewhere in e.g. older literature can look it up and get a clear explanation about it. If we just use "codomain" and "image" articles, I don't think it will be as natural to include that material, and it may either (a) get relegated to a less visible part of one or both articles, (b) be prominently discussed but somewhat distracting to the main point of the article(s), or (c) get skipped altogether or mentioned in passing in a way that doesn't really give readers the clarification they need. –jacobolus (t) 01:59, 6 December 2023 (UTC)

The proper place to discuss an article is the corresponding talk page, as most editors don't follow WikiProjects. Someone else had proposed the DAB at Talk:Range_of_a_function#Disambiguation some time ago; since there was no objection, I've implemented it. I'll repeat my arguments: the present article might mislead a causal reader into thinking there's a third unique concept involved, which is not the case -- "range" is just an ambiguous term for two concepts; furthermore, the fact that page is currently linked from a large number of articles is only one more reason why the incoming links should be retargeted to the unambiguous terms. PS: @Rodw: as you've started this thread, please consider making a note at Talk:Range_of_a_function. Also, the discussion is about a term, not a concept, so MOS:WAW applies; as such, it should be referred to as either "range" or range in the article (after MOS:ITALICTERM and MOS:BOLDREDIR). fgnievinski (talk) 02:11, 6 December 2023 (UTC)

might mislead a causal reader into thinking there's a third unique concept involved – I find this implausible. Much (much, much) more likely is that the disambiguation page or a redirect will leave a casual reader confused about what 'range' is supposed to mean. –jacobolus (t) 02:33, 6 December 2023 (UTC)

+1. --JBL (talk) 17:15, 6 December 2023 (UTC)

You're not going to concede not even about MOS:WAW, that you've reverted? [3] The article is about a term. fgnievinski (talk) 03:23, 7 December 2023 (UTC)

Sorry, my bad there. I was acting sloppily and misinterpreted what the change was (I somehow thought you were reverting back to the disambig page again, I think because I misinterpreted what you meant by the edit summary), and I used an inaccurate edit summary for the revert.

I don't think that the change is particularly helpful though, so I might still revert it with a different edit summary, or at least discuss further. I don't think we want to say "... the term range of a function ..." rather than just "... range of a function ..." in the lead sentence here, partly because the specific term is just range ("of a function" describes the context), and partly because this is inconsistent with other articles on Wikipedia, which may cause (very slight) confusion for readers. In my opinion we do actually want to describe the subject of the "range" of a function at this article and not purely the term per se, even though it's slightly ambiguous/inconsistent in usage.

Maybe there's some other better phrasing we could use in the first sentence. @Chatul, @JBL, @NadVolum, any ideas? –jacobolus (t) 03:40, 7 December 2023 (UTC)

I would change the emphasis rather than the wording: change the range of a function may refer to to the range of a function may refer to. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:04, 7 December 2023 (UTC)

But only a term could "refers to" a concept, so: "the range of a function may refer to" (or "the range of a function may refer to"). Otherwise, if the article were about a concept (which it is not), then WP:REFER should apply. fgnievinski (talk) 03:24, 8 December 2023 (UTC)

Having a discussion at talk:range of a function is also fine, but do note that WT:WPM has ~10x more page watchers, so is substantially more likely to get lively discussion from people who may care about this topic. Many short and relatively obscure wiki pages are of interest to a wider range of editors than those who bothered to explicitly put them on a watchlist. People often assume that an article that seems okay will just continue more-or-less as-is, which is why even dramatic and controversial changes like deleting a longstanding article and replacing it with a disambiguation page can go unnoticed until someone calls it to the attention of a bigger group. –jacobolus (t) 02:39, 6 December 2023 (UTC)

Thanks to everyone for contributions to this discussion. I don't know enough abut the topic to have a view, but I monitor various lists at Wikipedia:Disambiguation pages with links and notice when there are major increases. Often those with large numbers relate to templates used on multile pages and therefore wikiprojects, of people interested in the area, are generally the most helpful places to put requests for help. Not all projects are as active or helpful as this one, so I am really grateful for help.— Rod ^talk 08:00, 6 December 2023 (UTC)

I fully agree with range of a function being an article rather than being disambiguated. Image or codomain should be used instead in most references but if a user does come across range applied to a function then the disambiguation page wouldn't really do the job properly. It isn't like a user will always be able to distinguish easily in selecting the right disambiguation as would be the case if the other use might be range in statistic. The article clearly explains the difference and how in effect the term is now being deprecated because of the confusion. Range in statistics doesn't cause any confusion. NadVolum (talk) 11:20, 6 December 2023 (UTC)

There is a more subtle ambiguity than the obvious one. Some define a function as a set of ordered pairs, with the domain and range being implict; in essence that definition only allows onto (surjective) functions. Others take a categorical approach that includes an explicit domain and range. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 20:27, 6 December 2023 (UTC)

I tried to add some about how a unique surjective function can be defined given any non-surjective function. Do you want to add some material elaborating about the "implicit" definition of a codomain as image? Is there any good source (e.g. some expository essay somewhere) discussing the subtleties? –jacobolus (t) 23:03, 6 December 2023 (UTC)

Maybe a note that in Algebraic Topology and Homological Algebra the definition with an explicit range is more useful, due to the centrality of exact sequences. Or is that TMI? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:04, 7 December 2023 (UTC)

I have noticed that in logic they tend to use range for what in function theory wold be the image and not bother with codomains. And theorem provers may start off with the natural numbers starting at 1 which surprised me. NadVolum (talk) 12:40, 7 December 2023 (UTC)

0#Other fields

Would anyone like to try citing/cleaning up the "Other fields" section of the article on the number 0? Nothing in it looks egregious, but bringing that section up to par and not having a big maintenance banner on a high-visibility article would be nice. XOR'easter (talk) 20:27, 6 December 2023 (UTC)

I at first saw this as "zero sharp other fields". Disappointed. --Trovatore (talk) 20:47, 6 December 2023 (UTC)

Principle of maximum entropy

I am studying probability and I think the section Overview in Principle of maximum entropy is too high-level: it tells the interdisciplinary applications, but should be an outline of "how it works in practice" intuitively.

I added this new sub-section with what I have understood so far. It was deleted because the "tone" is wrong. Can someone check if the content is wrong? What do I do? Thank you. 62.98.166.30 (talk) 21:54, 9 December 2023 (UTC)