Tag management 2022

New year, new tag management thread.

Rules of the game are basically the same:

• A particularly bad tag (a rule of thumb: “if I can't imagine a person classifying a tag as either interesting or ignored, I'm getting rid of it”),
• A tag that should be a synonym of an existing one,
• A tag that used for two or more completely unrelated things,
• A need to create a new tag.
• Wait a couple of days before implementing a suggestion.
• After the problem described in an answer is resolved, please edit it to say so.

Also, note that one may use [tag:calculus] for , i.e. tags on the main site, and [meta-tag:discussion] for , i.e. for tags on the meta site.

Note that, in some cases, it might be better to have a separate question. Typically this happens when a longer discussion is needed and several possible answers are expected, since answers to a question provide more space for a more detailed discussion than comments under an answer in this thread.

• "Wait a couple of days before implementing a suggestion." - I assume this means working days?
– JMP
Feb 3 at 14:50
• @JMP What do you mean by "working days", if I may ask? Feb 6 at 7:39
• @TheAmplitwist; monday-friday.
– JMP
Feb 6 at 7:58
• @JMP In my mind, I did not make any distinction between the type of days. Feb 6 at 8:47

Proposal: rename to .

The term "data sufficiency" is quite vague, whereas the term "sufficient statistic" is a standard term in mathematical statistics and inference theory. In particular, a statistic $$T(X)$$ is said to be sufficient for a parameter $$\theta$$ if the distribution of $$X$$ conditioned on $$T(X)$$ does not depend on $$\theta$$. To my knowledge, there is no accepted definition of "data sufficiency".

If one looks at questions with this tag, they are mostly on the topic of sufficient statistics, so it's best if they now become properly labelled. Once this change is made, the tag info for this tag can be updated to reflect its current usage.

Proposed tag wiki: For questions about sufficient statistics. A statistic is sufficient for a parametric model if the distribution of the data conditioned on the statistic is parameter-free. For more general questions about statistics and estimators, please use .

• This looks like it should be a reasonably uncontroversial suggestion. Unless there is an objection, I will make the change next week. Do you have proposed tag wiki changes? Could you add that to your response here?
– Xander Henderson Mod
Feb 23 at 20:58
• @XanderHenderson Sounds good. I've edited my post to include a new proposed tag wiki. Feb 25 at 4:24
• Done. Thanks for the suggestion.
– Xander Henderson Mod
Mar 2 at 21:13

Proposal: Rename to .

I recently created for questions about co-hopfian objects in any category. I could have created which would be consistent with the pre-existing , but then questions about co-hopfian rings, modules, etc. would be awkwardly tagged with (I certainly don't think it's necessary to create , , etc.). Likewise, at the moment, questions about hopfian rings, modules, etc. would have to use the slightly ill-fitting .

I have created a tag wiki for and would be happy to update the tag wiki for to reflect the more general notion if the name change were to take place.

• Done.${}{}{}{}{}$
– Xander Henderson Mod
Apr 10 at 21:49

Merge the tags and under the umbrella . The latter has only recently been created and is not distinct from the former, at least not from reading the tag descriptions nor the usage of each tag.

Notice that all economics questions in MSE are really about mathematical economics. However, as is the case with the related tag, it is understood that these questions are about the mathematics of finance (see e.g. its tag description), which is why we don't have a tag.

Seems like , , and should be merged, perhaps into because that one is the most used of these three. They have nearly identical descriptions.

• At least from the tag descriptions, it seems like the latter two are about something specific in statistics while the first is just about the general process of estimating. Is that reflected in how the tags are generally used? (Apologies if this is a silly question, I don't see much of these tags myself.) Apr 11 at 3:34
• @KReiser The [estimation] tag is indeed used in more general contexts, so I modified my proposal. Apr 11 at 3:41
• Done. ${}{}{}{}$
– Xander Henderson Mod
Jul 27 at 21:27

Proposal: Create a tag, to be used in conjunction with .

Most questions with the tiling tag ask whether some tiling is possible, or ways of finding solutions to a particular problem, while questions about Penrose tilings are usually much less about problem-solving and instead about proving properties of the structure, or looking for guides to different constructions, programmatic generation, etc. Giving an additional tag to these fairly common questions (a substantial fraction of all questions under the tiling tag) seems useful.

Proposed tag wiki: Use this tag for questions about the family of Penrose tilings: their combinatorial structure, construction methods, the empire problem, and related material.

• +1 Limiting the search query to only Questions is (to me) a better measure of the topic's frequency. Aug 21 at 12:16

Proposal: Create and untag questions from /.

I was recently looking through and noticed most of the questions are actually about intervals, not interval arithmetic, likely because it and are the only tags that pop up when one attempts to use , which doesn't exist. I didn't look at as much, but it looks less severe than .

Proposal tag wiki: Questions about intervals. A (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

Definition taken from Wikipedia.

This question on main has the tag and is the only question with this tag.

I think it should be renamed but I'm not sure how to do it. Or it could be removed altogether.

Proposal : Create tag

A function $$f:(X,\tau)\to (Y,\tau')$$ is a Darboux function if $$f(C)\subset Y$$ is connected whenever $$C\subset X$$ is connected.Examples include all continuous functions.

If we restrict our attention to the real valued functions of real variable then functions having intermediate value property coincides with the daboux functions.Now we can extend the class of Darboux functions by including derivatives of a differentiable function ( another interesting theorem : derivative of a differentiable function is a Darboux function)

Continuous function and Darboux function:

Continuous functions have the Darboux property. But converse isn't true.For an example we can take a differentiable function which is not continuously differentiable.Infact $$f_n\in C(\Bbb{R}$$ defined by $$f_n(t) =\begin{cases}t^n \sin (\frac{1}{t})&t\neq 0 \\0 &t=0\end{cases}$$

Then $$f'_n$$ for all $$n\ge 2$$ is a sequence of discontinuous Darboux functions.

Theorem: If $$X$$ is Hausdorff, locally connected and Fréchet, and $$Y$$ is Hausdorff (e.g. if $$X=Y=\mathbb R$$), then any preserving function $$f:X\to Y$$ is continuous. ( MO post)

There is also interesting study related Darboux functions with :

1. aditive functions ( solution of Cauchy functional equation).One interesting result, any additive onto functions either injective or has the Darboux property.

2. Convex functions,

3. Baire functions ( Conway base 13 function which is in Baire class $$2$$ but have the Darboux property.(thanks to J.H.Conway).

4. DARBOUX LIKE FUNCTIONS with some interesting open problems.Ohh great stuff. Still so many unknown places to discover.

To add more strength to the questions related to Darboux function or Darboux property, I think it would be better to add tag like along with two common tags and .

• You claim to have seen "a lot of posts associated with Darboux function". Perhaps you could link to some of these. It would also be helpful if you could describe what the tag wiki might look like. How is such a tag meant to be used? What kinds of questions fall into this tag?
– Xander Henderson Mod
Jul 27 at 21:24
• How did you get the number 1159? If you simply used the search with the keyword Darboux function, notice that this includes both questions and answers. If you restrict that search to questions, the number drops to 521. (And, of course, not every question containing these two words is about this topic. At the same time, intermediate value property seems to be other common terminology. Jul 28 at 2:30
• Sourav Gosh, Phd in Darboux functionology Aug 20 at 21:56

I would like to propose the tag [bump-function] with the label: use for questions related to bump functions, which are smooth functions with compact support. They are non-analytic, and are used as mollifiers and to create smooth partitions of unity, among other uses in analysis.

I have learned from these functions recently through questions here on Math Stack Exchange, and at first I was really lost about them, partially because at first I don´t fully understood its definition on Wikipedia, and because I am trying to use them for a completely different purpose as their use as tempered distributions, mollifiers, and weak derivatives (main uses I found on the questions), but instead, as possible finite-duration solutions to differential equations, as they are defined in the paper "Finite Time Differential Equations" by V. T. Haimo (1985) (is quite interesting by the way, if you want to check it).

I believe the tag is going to be useful since smooth-functions is to general and is quite non-intuitive (at least for me), that there exists a class of non-analytic examples. As example of the use I am interested in, all them ends with an "aggressive" exponential behavior, which make a lot of sense thinking of them as possible exact solutions to the nonlinear pendulum with friction, which is commonly solved through an exponential function in the small-angle approximation.

I hope it made sense also for you, an apologies in advance if it not fulfill this site standards (and for grammar mistakes since English is not native for me).

Best regards.

• Some related discussion in the tagging chat room recently (see here) Feb 24 at 22:12
• @ArcticChar thanks. I paste the opinion here following an instruction from an inmail I received (it was my answer to it). I am not familiarized with chat rooms, neither with the website standards so I hope you understand the mess I made was with the intention to help, as for me was difficult to understand the topic at first. I hope, if the tag is not added, that at least where considered into the synonyms, since they are useful for searching for related answers after submitting a repeated question... at least from my experience (which is the view from a new user), they are very helpful. Thnx. Feb 25 at 0:25
• Tags should serve to create some kind of taxonomy of questions, and group together questions which might otherwise not easily group together. What does at bump-function tag offer which is not already accomplished by searching? or searching? How does this tag help to organize the site?
– Xander Henderson Mod
Feb 25 at 3:36
• @XanderHenderson From someone who knows the topic he is looking answers, I am agree with you that it is going to add too little... but from the point of view of someone that is looking for first time a topic, that sometimes don´t fully understand where the search is going neither the jargon involved on the topic, related labels helps to looking for branches in the line of thought you math intuition is driving you: actually in this way I found the bump function as possible example of finite duration solutions, since as engineer, I have never heard of them before. Feb 25 at 3:50
• You appear to be proposing the tag bump-function here. Can you find any examples of posts which would be tagged with this tag, but which do not contain the text "bump function" somewhere in the question?
– Xander Henderson Mod
Feb 25 at 14:17
• Just search for "smooth non-analytic" here Feb 25 at 15:30
• It is not obvious to me that any of those should be tagged bump-function. Please, don't make me do all the work of arguing your case for you. Give me some concrete examples.
– Xander Henderson Mod
Feb 25 at 15:44
• As example, the second result is using as example a bump function without now it, not even mentioned in the comments neither on the answers. It looks like they are widely known among mathematicians, but as someone is not in that category, I could tell they are widely unknown, at least among engineers. You need to understand I have the view of someone that just discovered them, with basic math knowledge (I am an electrician). And now I feel guilty because of taking that much of your time XD. I just give my opinion. Feb 25 at 16:05
• That question is about showing that the particular function they are looking at (which happens to be a bump function) is not analytic. The fact that the function is a bump function is not really relevant, particularly if you consider that the tags should reflect the knowledge and level of the asker, and shouldn't simply reflect the presence of particular objects. By your reasoning, we could just as easily add the tag piecewise-function to that post, as it happens to involve a piecewise defined function.
– Xander Henderson Mod
Feb 25 at 16:16
• Actually, I am asking about the existence of non-piecewise bump functions here, since they are the similar thing I could find so far to a "finite duration solution" to an ODE... piecewise functions are different from them, is one of the things I would like to point with these and the other tag. But again, I am probably wrong. You are in charge, if it dont fit the site standards, well, bad for me. I really appreciate your dedication to this topic, thanks you very much for your time. Feb 25 at 16:24
• Just to add a follow up: even that bump functions could be finite-duration solutions to some nonlinear ODEs (IVPs), there are finite-duration solution that are not bump-functions: I believe that the eq. $\dot{x}=-\text{sgn}(x)\sqrt{|x|},\,x(0)=1$ has the nontrivial solution $x(t) = \frac{1}{4}\left(1-\frac{t}{2}+\left|1-\frac{t}{2} \right|\right)^2$ (this because of Local Existence and Uniqueness of solutions of ODEs). I read in the Tag chat that in addition to the bump-function tag also Mollifiers tag was deleted - It is possible to added them as Synonyms under the tag "smooth-functions"? Mar 14 at 1:55

New tag suggestions:

• "class-theory" for questions about foundations of set theory from the point of view of the various class-theoretical extensions of axiomatic set theory (Morse-Kelley, NBG, ZF, etc.)
• "errata-in-published-works" for questions about "Is this an error I see before me, the pages toward my eyes?"

Proposal Add the tag proof-by-contradiction

or a similar wording;

• We have no tags for types of proofs. Why should we create a tag for proofs by contradiction? Apr 7 at 21:27
• Apr 8 at 3:50

Maybe not the best example, but my question here is about verifying a claim, not a solution or a proof. I don’t find any other fitting tags for such a question.

Proposal: Add the tag [tag:foundations-applied-math]

The mathematician Norman WildBerger has been stressing on his YouTube channel (https://www.youtube.com/c/njwildberger) his non-belief in infinite sets and also the real numbers and their associated arithmetic operations. That is Real numbers requiring infinite decimal places to define them. These "Real" numbers including irrational numbers like $$\sqrt{2}$$, $$\pi$$ and $$e$$ are really notional numbers to the Applied Mathematician since we can only in practice carry out arithmetic operations on rational approximations to them.

Dennis Morris in "Even Mathematicians and Physicists make Mistakes" has questioned many existing mathematical structures used in Theoretical Physics and Applied Mathematics. He wants to distinguish between axiomatic mathematical systems and finite mathematical systems deriving from the number one. At the moment his system is not complete and largely remains unproven.

Further back R.L. Goodstein and others tried to develop a finite number based foundation for mathematics as a whole using recursive numbers.

Many of the questions up in the air today resolve around questions such as: What is the relationship between the finite permutation groups and the elementary laws of particle physics? Does a well founded system of applied mathematics properly constrain physics because the universe is ultimately mathematical in nature or is the mathematics (group theory in particular) misleading us as to the true nature of physics?

The current state of affairs over the foundations of applied mathematics appears extremely unsatisfactory to me. If there is a theory of finite mathematics underlying science, engineering and computing to be uncovered, then it is hardly ideal to found it on the basis of infinite sets and mathematical operations on real numbers with unlimited decimal places. If nature has more subtleties that current known mathematics can describe, then we should perhaps be clearer in regard to the foundations of applied mathematics as a first step to develop something better.

Lots of interesting claims are being made, which may turn out to be wrong or have entirely different scope and limits to what the author of the claim believes. (Interesting meaning - thought provoking even if later proved wrong.)

I admit that the foundations of applied mathematics could be classified as an under-developed mess with ongoing research definitely required - therefore it should be strictly speaking the remit of MathOverflow. However I do not know if there are enough applied mathematicians frequenting MathOverflow for this tag to be of interest to them. MathOverflow do not appear to have a tag suitable for questions targeted at the foundations of applied mathematics yet, although unlike math.stackexchange they do have the tag [applied-mathematics].

• Are mathematicians here happier to change the accepted foundations of pure mathematics, to consistently and satisfactorily encompass applied maths, rather than risk a potential schism with two foundations circulating simultaneously, one for pure maths and one for applied maths? I think that is ultimately the better path to follow. Jan 30 at 22:02
• This is an editorial. Wildberger appears on YouTube. So does Mick Jagger. That doesn't make either of them credible mathematicians. Jan 31 at 1:12
• Disregarding that I don’t agree with the premise. My sense is that we do not add tags to dictate or promote what Questions should be asked. So this is the wrong place to evangelise. In addition the comment about MathOverflow is irrelevant. Jan 31 at 6:04
• @CalvinKhor: if tag[foundations] encompasses all theories as to the foundations of mathematics (both pure and applied), and including both monist and dualist frameworks, then why is there a tag called [univalent-foundations]. That tag is serving the purpose of promoting one popular foundational approach over others. Whether a question under tag [foundations] is considered acceptable and within scope is a matter for consensus opinion. And tag consensus reviews are an implicit input to that. Therefore consensus rules all on this site and I am fine with that. Thanks for the feedback. Jan 31 at 14:13
• Among possible reasons: because there are questions about it, and hence a tag makes them easy to find. Where are the questions regarding what you are proposing? I don't think any applied mathematician is worried about such a "schism". Nevermind that the very concept of "foundations" is something for a "pure mathematician" to worry about. Jan 31 at 15:23
• This seems just to be Finitism; it's not a new concept. I'm sure if you want to ask some questions about Finitism, or request answers from the point of view of Finitism, you can use the foundations tag. I would just strongly caution against using this site as a platform for proselytising. Feb 4 at 6:45
• @TheoBendit: If you take the symbol for multiply "$\times$". It implies an unspecified general algorithm that works with integers, rational numbers and irrational numbers to any arbitrary precision. Norman Wildberger is asking for example how do we define $\pi$ and $e$ in consistent fashion to any arbitrary yet to be chosen decimal approximation, and at the same time obtain a provably general algorithm to calculate a number like $\pi \times e$ with a output in the same consistent form and with the same arbitrary precision as the two original input irrational numbers. Feb 4 at 9:20
• @TheoBendit: This is a legitimate point of view to be investigated and for valid mathematical questions to be asked. The wikipedia page on Finitism gives a distinctly more philosophical point of view rather than the more modern algorithmic point of view of applied mathematicians. Feb 4 at 9:31
• If this is what Wildberger is asking, then he's not a mathematician. And should study basic real analysis if he cared. Wake me up when a bridge or skyscraper falls down because we didnt agree on the value of $\pi\times e$... Feb 4 at 9:39
• @CalvinKhor: It so happens that the theory of lift and flight has been refined since I when to university. Of course the flying properties of existing planes do not change because the theory of lift has changed. It is not unreasonable that some people want to investigate foundations of mathematics from an algorithmic and finite point of view. If you define mathematics in such and such way, then there is a set of allowed mathematical questions together with a residue set of non-mathematical questions, Change the foundational definitions then the sets of allowed/disallowed questions can change. Feb 4 at 10:03
• @JamesArathoon Finitism absolutely is a legitimate mathematical concept (I didn't mean to imply otherwise), and you and WildBerger are entitled to your opinions about how applied mathematics should be run. I'm just saying, it is ill-advised, when asking a mathematical question to which you expect a finitist answer on this site, to use the platform to try to convert people to your viewpoint. I would vote to close such a question (something I personally rarely resort to). I would do the same if anyone went on an anti-finitist rant as well. This is just not the site to do such things. Feb 4 at 20:29