# Tag management 2020

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.

• Even though we have a tag management thread, it's worth pointing out that in some cases it might be better to have a separate question. (Typically when a longer discussion is needed and several possible answers are expected. Answers to a question provide more space for a more detailed discussion than comments under an answer in this thread.) – Martin Sleziak Jan 6 at 1:19
• @gen-zreadytoperish Sure. I missed that. – José Carlos Santos Jan 8 at 15:59

Resolved. renamed to .

Proposal: Rename to .

Although Lothar Collatz is most known for the $$3x+1$$ problem (the Collatz Conjecture), I don’t think their names should be used interchangeably. Furthermore, the latter tag has a more informative name.

I posted this in the last Tag Management, but I only got a single upvote. I want to see what more people think. (Also, since gaining rep in that tag is pretty hard, I don't have the ability to propose the synonym myself).

Proposal: Create the tag .

The Eulerian number $$A(n,k)$$ is the number of permutations in $$S_n$$ with exactly $$k$$ descents, and it is an important combinatorial object.

Searching for "Eulerian numbers" is:q returns around 30 legitimate hits, which is a worthwhile number of questions to have a tag attached, in my opinion.

I had also raised this request in the Tagging chatroom a few months ago.

Update: It has been ten days since this was proposed and it looks like the community approves it. So, I've gone ahead and added the tag to the three oldest relevant questions I could find. I've also added a wiki and excerpt.

• I like the tag and wouldn't mind seeing it applied to some more questions. – Alexander Gruber Jan 14 at 19:25

Proposal: Remove , .

These are meta tags with very bare-bones tag wikis. Furthermore, there aren’t any other tags for important math exams, i.e. the IMO or USAMO, so why should we make an exception for these two?

• Posts about these tags in older tag management threads: 2014, 2016 and 2017. – Martin Sleziak Jan 10 at 3:39
• @MartinSleziak Good to know this issue has been raised before. – URL Jan 10 at 3:39
• These questions are also somewhat related: Tag request: csir-net-exam and Would a qual question tag be useful? (There was also this suggestion, the question was deleted: Tag request - GATE Exam.) – Martin Sleziak Jan 11 at 13:42
• It is worth pointing out that USAMO and IMO are not really exams (or at least I would consider them contests rather than exams). We have a tag (contest-math) suitable for question from USAMO, IMO and other contests. – Martin Sleziak Jan 11 at 13:43
• @MartinSleziak The key difference between contest-math and the tags I suggest removing is that the former gives very important context. Some very hard problems without the tag could easily be dismissed as open, or inaccessible; moreover, contest math problems are almost always contained in four well-defined topics. The more straightforward nature of the problems in the GRE, GMAT exams, as well as their higher variability (from what I've seen; this is very arguable), makes their tags much more unnecessary. Even if you wanted to consider these two at the same level, I'd suggest a merge. – URL Jan 12 at 4:48

Proposal: Create a tag .

In this question the asker asks why there is no tag for questions related to the umbral calculus. I am in agreement with Alexander Gruber's comment that the significant number of otherwise unorganized questions on the topic is a good indication that the tag is needed.

Proposed Tag Excerpt:

Umbral calculus refers to a method of formal computation which can be used to prove certain polynomial identities. The term "umbral", meaning "shadowy" in Latin, describes the manner in which the terms in discrete equations (e.g. difference equations) are similar to (or are "shadows of") related terms in power series expansions.

• I am not expert enough to write a better tag except, nor a long tag wiki. I invite modification, and have marked this answer Community Wiki. – Xander Henderson Feb 20 at 14:57
• The proposed tag has been created. – YuiTo Cheng Apr 24 at 13:43

Proposal: Eliminate the tag .

The tag is too broad—there are a large number of things in mathematics called "transformations" coming from diverse parts of mathematics, and tagging a question with this tag does nothing to refine or sort these different notions. I would like to see this tag dead and buried.

I have spent the last month working to either retag or delete questions which have this tag and no other—there is only one remaining question in that category (and that question appears to be on its way to deletion); please see the pertinent SEDE query (thank you, Martin Sleziak, for bringing this query to my attention).

Proposal: Remove the new tag . I think it is easily abused and not particularly useful (doesn't convey any interesting information to answerers).

• Just to clarify: I saw this answer after I've done the clean-ups (here and here). I think in this case it is pretty clear that the new tag doesn't do any good to the site. – YuiTo Cheng May 2 at 1:40

Proposal: Merge and .

I'm no statistician, but I don't see the value in having both tags. Looking at the questions under , there doesn't seem to be anything that doesn't fall under the tag .

• Outside of probability theory, "Gaussian" typically refers to a curve $a \mathrm{e}^{-bx^2}$, give or take. This is related to the heat kernel, is important in the study of Schwartz (and other functional) spaces. I think it might be better to preserve the two tags, but edit the gaussian wiki to better highlight the distinction. – Xander Henderson Mar 3 at 14:33
• And, now that I have had time to look at the questions: there are 10 questions tagged gaussian. Only one of those is not a prob and stats question (though there are two or three others which are general enough, perhaps, to deserve a "Gaussian" tag in the sense I proposed). Perhaps the gaussian tag serves no purpose and should be merged. :\ – Xander Henderson Mar 3 at 16:20
• @XanderHenderson I agree. The tags are used in conjunction. – Don Thousand Mar 3 at 16:37
• @XanderHenderson So what should be done about the tags? – Don Thousand Mar 4 at 14:52
• I don't have a good answer to that question. Given that only ten questions are tagged gaussian, and nine of those are prob & stats questions, I wouldn't object to your proposal of merging the tags. – Xander Henderson Mar 4 at 17:36
• @XanderHenderson Unfortunately, I can't propose the merge, but the Gaussian tag is getting bigger... – Don Thousand Mar 6 at 14:20
• Just to clarify, are you suggesting merging with or without a synonym? (Or did you want to suggest a tag synonym rather than merging the two tags?) See also: What is the difference between merging two tags and synonymizing two tags? and What is the difference between a synonym and merging a tag? – Martin Sleziak May 2 at 11:39
• @MartinSleziak I think gaussian should be a synonym of normal-distribution, since the latter is the more established tag – Don Thousand May 2 at 16:10
• It seems a lot of the questions under gaussian are about the Gaussian Process. How about changing the tag to gaussian-distribution and making it a synonym of normal-distribution, and then questions that aren't about the Gaussian Distribution can be tagged more precisely, e.g. gaussian-process gaussian-integral gaussian-clothing – jeremy909 May 31 at 16:47

Rename to . (Also a name such as (calibrations-differential-geometry) - or something similar - would help with clarifying the content of the tag. However, that seems to be unnecessarily long.)

The tag was created in June 2019. This is the question where the tag was created: Calibrations vs. Riemannian holonomy. From this question it seems that the intention was to created a tag for calibrated geometry. As the tag name can be interpreted in several various ways, it is not surprising that questions from other areas appeared there too. For example, the most recent question is Camera calibration problem - computer vision. List of the questions which had the tag at the time when I posted this answer can be found in chat.

If the tag is renamed, it is more likely to be used consistently.

• A possible alternative would be to removed the tag for callibrations (or callibration geometry) completely, if users more experienced in this area consider the tag unlikely to be useful. – Martin Sleziak May 10 at 5:34
• Not sure if it is calibrated geometry or calibrated geometries. The latter one is used in the oriiginal papers where calibration was introduced. There are several different such geometries. – Arctic Char May 10 at 20:24

Proposal: Remove . It's a duplicate of

Proposal: Rename to .

I added a tag excerpt/wiki a few months ago to specify that this isn't just a tag for any limit that you graph, but I've edited the tag out of a lot of questions that used the tag as such. I think that renaming it would remove this tendency.

# Proposal: add a tag for exponential families

Rationale: I've asked at least a couple of questions now that I originally tagged with , but each of these were edited to remove the tag. However, I think such a tag deserves to exist, because the concept of an exponential family is absolutely crucial to a number of topics in statistical inference and machine learning. Moreover, it's a somewhat subtle concept that students can often trip over - exponential families have a number of important non-obvious properties, and they are generally the first place where you start having to reason about manifolds of distributions, rather than just considering one distribution at a time.

Additionally, when I find myself asking about exponential families, there isn't really any other tag that fits the question. I can use , but that's too specific - it emphasises only the geometric perspective on exponential families, while a more classical inference perspective might be just as useful. I can also use , but that's too general, because you can read a lot about information theory without ever meeting the concept of an exponential family. Consequently, it's difficult to find and identify questions about exponential families without a specific tag.

Searching the site for "exponential family" reveals a reasonable number of questions on the topic (at least, most of the ones on the first page are actually about exponential families), but they are tagged with a random mixture of , , , , etc., which suggests that a specific tag for this topic would be helpful.

(An explanatory note, in case it's needed: people sometimes say informally that normal and lognormal distributions are part of "the exponential family." I don't intend the tag to refer to this but to the concept of an exponential family, which has a precise technical definition and refers to a set of distributions that's parameterised by a vector of real numbers in a particular way. I suppose the tag wiki would need to make clear that the tag is intended to be used this way.)

• I have added a Wikipedia link (in case it is helpful to clarify the notion you're talking about). I have collected the previous instances that I was able to find in the Tagging chatroom. – Martin Sleziak Jan 14 at 18:54
• Would it make sense to call it exponential-classes? Though that is (according to the wikipedia article) a less common term, I think it may be less prone to misuse than exponential-families. – Alexander Gruber Jan 14 at 19:21
• @AlexanderGruber I'm hesitant, because I've never heard that term, and I'm familiar with quite a lot of literature that uses them – Nathaniel Jan 14 at 19:41
• @Nathaniel do you know of any other synonyms? – Alexander Gruber Jan 22 at 7:20

Please create the tag "realizability" for questions regarding realizability as the term is used by researchers like Kleene, Kreisel, Troelstra and also in more modern work on proof theory.

Looking through posts that use the word "realizability", the term is sometimes used to refer to the term from proof theory, and sometimes in a seemingly colloquial manner to refer to arbitrary mathematical concepts to be somehow "realized". So, having a well-defined tag for the proof theoretical term would help getting more relevant search results when searching for the tag.

Suggested tag definition wording (editing is welcome):

Realizability is the proof theoretical study of formal objects (realizations) that realize formulas from a formal theory, giving knowledge about the truth of the formula.

• It would help if you discussed the use of the term "in completely different contexts", and what distinctions could be drawn. If you think the tag summary would help users to properly apply it, your proposed language could be added to this post. – hardmath Jan 11 at 17:30
• @hardmath: I was referring to the findings of Noah Schweber from full-text searching in the original post. I put it more precisely now. Actually, the proof theoretical term is the only one where I know it is somewhat defined (even having a Wikipedia article). Of course, if there are other areas it mathematics which use the term in a well-defined manner, it should probably be discussed here to be able to distinguish. – ternary Jan 13 at 6:59
• There's a LOT of different uses of the term realizability. Is there a way to narrow it down, maybe proof-realizability? – Alexander Gruber Jan 14 at 19:27
• @AlexanderGruber: I think this is even better that my suggestion. – ternary Jan 14 at 21:02
• I must say I think it's kind of rude to downvote the original tag suggestion question. After all, the math.stackoverflow UI explicitly tells new users to ask here on meta (and not to answer somewhere on meta). I agree that it is sufficient to discuss things in one place, but there is no comprehensible way to call the original question a "bad" question. – ternary Jan 20 at 14:59
• I'd like to add that mathoverflow already has a "realizability" tag. Maybe it does work with a proper definition. – ternary Jan 20 at 14:59

Proposal: Rename to geometry-probability.

This is to make it distinct from questions about geometric random variables.

$$\textbf{Proposal}:$$ Create the tag Quotient-ring

Searching for "Quotient ring" is:q returns 1010 results.

There is also a tag quotient-group, so I thought that there may be one for rings too, given that is common to see a lot of questions about identifying quotient rings with some known ring, ideals, etc. The tag quotient-space seems too general.

It does not make sense to create a tag for each quotient structure, but at least in groups and rings are very "popular" or common I think.

Proposal: Cancel the synonym complex-analysis and holomorphic-functions tags

The holomorphic-function tag synonym was proposed in May 2016. It was approved in March 2019. (Information thanks to Martin Sleziak)

Currently there are 6,698 questions about complex-analysis and 4689 questions about holomorphic-functions, it seems to me that would be appropriate to have a separate tag to classify questions better.

• I will point out that the two tags are synonyms - they were not merged. So you probably want to ask to cancel the synonym (ton to unmerge). For people who want to check how cancelling synonym works: What happens with the tagged questions when a tag-synonym is cancelled? – Martin Sleziak Jan 14 at 1:00
• duh..I will edit, thank you Martin – Bellatrix Jan 14 at 1:01
• I will also add links to a related conversations in Math Mods' Office and the exchange in the tagging chatroom. Among other things, people can find there this SEDE query which shows the dates 2016-05-28 (CreationDate) and 2019-03-23 (ApprovalDate) for this synonym. – Martin Sleziak Jan 14 at 1:03
• What is the purpose of having a separate tag for holomorphic functions? To a very good approximation, complex analysis is the study of holomorphic functions. – Eric Wofsey Jan 14 at 3:19
• @EricWofsey I agree with your comment but also notice that there's approximately a difference of 2,000 questions that aren't about holomorphic-functions – Bellatrix Jan 14 at 19:20
• @Isabellatrix Some questions mention "analytic functions", which in complex analysis is equivalent to "holomorphic functions". Also, if you search for just "holomorphic" (without "functions") you get 6657 results... – Arnaud D. Jan 15 at 10:53

# Proposal: epsilon-delta$$\rightarrow$$limit-definition

Following a suggestion posted here as a comment, I suggest that we rename the epsilon-delta tag as and that becomes a synonym for that tag.

• At first I thought this is a good idea. Yet if somebody would ask something like: "Use the epsilon-delta definition of continuity to prove directly that $x \mapsto x^2$ is a continuous function on $\mathbb{R}$." then the former seems natural as tag yet the latter maybe not so much. Thus, I am now a bit on the fence about this. – quid Apr 24 at 10:02

Proposal: Merge and tags.

The idea behind having two tags is to divide basic and advanced probability questions, but it does not work and I believe it couldn't work. It is better to have single tag and use additional tags like , , etc.

PS: Downvotes show that is like a suitcase without a handle: hard to carry but a pity to throw away.

• Older related posts: About [probability-theory] tag and The tags (probability) and (probability-theory). As you said, both tag-info and a related comment template suggest to keep them separate. I have tried to summarize this also in the tagging chatroom. – Martin Sleziak Jan 8 at 7:24
• Regarding the recent edit, it is probably possible to maintain a pair of such tags - but for that some users who will follow the tag will be needed. For example, (elementary-set-theory) and (set-theory) are in quite good shape since there are users who follow them very closely and retag the questions when needed. – Martin Sleziak Jan 9 at 8:44
• Do you think that renaming the tag to (elementary-probability) would it make more likely that people would be using the tags correctly (i.e., in the way they are described in the tag info)? Currently (elementary-probability) is a synonym of probability, with (probability) as the master tag. – Martin Sleziak Jan 9 at 8:46
• @MartinSleziak I don't think that retaging questions by other users is good idea; also I don't think that the current status of probability-theory tag as an alternative to probability tag is a good idea; anyway, it does not work in practice. I think probability-theory can be used either as a secondary tag for the main probability tag, or simply removed. And there is no need in elementary-probability tag. – kludg Jan 9 at 9:37
• Elementary probability problems and more advanced probabilistic concepts should definitely not be merged. These are handled very differently and require very different levels of mathematical knowledge. As an analogy: imagine if we merged number-theory and elementary-number-theory – what a disaster that would be! – URL Jan 9 at 19:21
• @URL How this is related to the particular probability and probability-theory situation? In no way. I believe most downvoters rarely or never visit probability questions, and don't understand why probability-theory tag is not needed. – kludg Feb 20 at 15:42
• I wouldn't merge them, but renaming probabilty as elementary-probability seems to be a good idea. After all, it states "For basic questions about probability [...]". – Jean-Claude Arbaut May 5 at 7:35