3:08 AM
Lot of things here, I am not sure whether I will be able to respond to all at once.
@quid Let me try write something about and .
I am not sure it's a good idea to have this synonym. The point is that there are plenty users that need to find (local) maxima or minima of some function (in a calculus context), Now one could shoe-horn this into being a question about optimization, but I am quite doubtful this is a good idea. Instead I'd keep this, and syn max-min with as well as extrema, the -ation variants can stay syns of optimization. — quid 7 hours ago
Actually I think this is good illustration what exactly is our difference of opinion. You are saying that extrema and optimization are not the same thing. And I certainly agree that common use of the words is different. (When hearing those two words in conversation, I would expect different thing.)
However, on this site it has been long established that the tag (optimization) is supposed to be used for this type of questions. It is mentioned on meta, it is clear from the fact that synonyms exist. Ideally, it should be make explicitly clear also in the tag-wiki.
So even if it is not clear from the name of the tags that two tags are the same, if there is semi-official consensus (from meta, tag-info, approved synonyms) that on this site we consider them as the same (or as one of being subset of another) I use the tag accordingly. (And probably so do other users, if they read information in the tag-info, meta or if they add the tag via synonym.)
And of course, if the community here changes agrees on something different and says that the usage should be changed, I do my best to follow new consensus when tagging the question. (And if I have time I try to help with retagging the old ones.)
In this particular case, I think it will not be easy to revert the current usage.
But the tag was used for questions about finding already before that. When I posted question on meta, I mentioned the observation that it is used this way and asked what should we do in the future.
For example, if you search for questions tagged lagrange-multiplier+optimization you can find usage of this tag preceding that thread. I will add two examples from 2012 here and here.
So if this is to be changed, I guess it would take some effort to retag the question which has been tagged like this since 2012. And since it is a change which affects, it should probably be discussed on meta first.
For the time being: You might downvote the synonym, so that it is removed from the list of tag synonyms while still being discussed. (Perhaps I should not have suggested the synonym without asking on meta, but since we already had all those other synonyms which are almost the same, it looked clear-cut case to me.)
And until this is resolved one way or another, I will be try to use both tags (to comply both with the current practice and with your suggestion that (maxima-minima) should be kept separate.)
Perhaps this will be more readable if each "block of messages" I add are about one topic. So I try to respond to other things you have mentioned later. This is basically what I can say immediately about issue. And, as I said, it also illustrates why we disagreed on separation axioms and separability.
I will perhaps also mention than when I add optimization tag in this purpose, I often say so also in the edit summary, see this SEDE query.

3 hours later…
6:29 AM
I see that Michael Hardy created tag here:
4

Let $Y_1, \ldots , Y_n$ be a random sample from the uniform distribution on the interval $(0, \theta)$ with an unknown $\theta > 1$. Suppose we only observe for $i = 1, \ldots , n$ $$X_i= \begin{cases} Y_i & \text{if } Y_i \leq 1, \\ 1 & \text{if } Y_i > 1. \end{cases}$$ Find the Method of Mom...

I did not know that such thing exists:
In statistics, engineering, economics, and medical research, censoring is a condition in which the value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is at least 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75. Censoring also occurs when a value occurs outside the range of a measuring instrument. For example...
@MichaelHardy I see that you have create (censoring) tag. it might be useful to create also tag-wiki or at least tag-excerpt. It might help other users to use the tag correctly. Another reasons is that the tags used on only one question are automatically deleted after certain time unless they have tag-wiki. — Martin Sleziak 39 secs ago

2 hours later…
8:19 AM
What would be good tags for this question?
0

If $n = 5$ then $$\left\lfloor1\sqrt{2}\right\rfloor+ \left\lfloor2\sqrt{2}\right\rfloor + \left\lfloor3\sqrt{2}\right\rfloor +\left\lfloor4 \sqrt{2}\right\rfloor+ \left\lfloor5\sqrt{2}\right\rfloor = 1+2+4+5+7 = 19$$ Sequence from $1$ to $20$ is: $S=\{1,2,4,5,7,8,9,11,12,14,15,16,18,19,21,22,... I have just retagged it with , , . And I have also added , since this might be right tag for questions about Beatty sequence. If you look at revision history the OP used originally , and . They were removed in the second revision but they were added back in the third one. I'm not sure whether it was intentional or whether it was result of a clash between the previous edit and this suggested edit. Anyway, if you can see better tags of if you see why the tags I removed are really relevant for that question, please go ahead and edit it. 4 hours later… 12:52 PM @MartinSleziak Maybe. But it should not be like this. The tagging system must not have any relevant learning curve. Usage on the site should match common usage as much as possible. re Lagrange multipliers, that can very reasonably by tagged optimization. Usually the idea there is to actually to optimize in a way. @quid I have mentioned Lagrange multipliers just an easy way to find such questions. Try the tags calculus+optimization and you will find questions tagged that way before the meta thread. Or you can simply take my word for it, that when I posted that on meta, it already was a relatively common way to tag them. By contrast calculus students investiganting some function and determining "interesting" points and features, like poles, roots, tangents, saddle points, and well (local) extrema, are not suddenly doing optimisation when it is about the last. Just one example when the tag is used like this in 2011: math.stackexchange.com/posts/9171/revisions They might be doing optimisation. That last example, is more optimsation than what I said. Considering that there are 8k questions tagged (optimization), if the tag are going to be desynonymized (is that even a word?), retagging of old questions is not a one-day job :-) 12:57 PM As mentioned in the topology discussion just to avoid future problems is also good enough. Moreover, max-min could reasonably by used in quite different ways too. What is the max of this set {some reals numbers written in different ways}. Ok, I will probably stop looking for old questoins. What I agree is that max-min and maximum-minimum should be treated in the same way. Anyway, we have a thread on meta saying that the current consensus is using optimization for questions about finding maximum or minimum. So probably you should first try to gain some support on meta to change this. Yes, we also have digits as a synonym of decimal-expansion. I was pretty shocked to find out about this yesterday. It makes no sense at all. Although sometimes I have feeling that rather than discussing things on meta, it would be easier if the tag system would be considered dictatorship. (And probably some users use tags in this way.) However, how to decide who would the dictator be. 1:02 PM @MartinSleziak there are relatively few users involved so it is some kind of oligarchy. @quid Before switching to another topic, do you plan to do something about optimization issue? Personally, until some this is discussed on meta, I still consider (optimization) the correct tag. Here "correct" means "in accordance with community consensus and guidelines on meta". @MartinSleziak just to understand your position, you consider optimisation a correct tag for "What is the maximum of the set {\sqrt{3}, log_2 (3) , 3/2 }"? Thus to tag this maximum is also incorrect? Although if you take the way that meta post is phrased literally, then I should agree that it fits. I should have put more thought into that meta question when I was posting it. :-( I would certainly not add tag (optimization) to your example. I might add (inequality). (If I was about to tag such question.) @quid I am glad that we agree on something at least. 1:15 PM @MartinSleziak I might lobby for the max-min being unsyned. Not sure if I'll actually do it. I think to common terms just do not make much sense as tags. But it just hides the problem to map them into something. Instead, I am in favor of blocking them completely or to keep them around with a wiki explaining what should be used instead in the different use cases. Ok, so at least two examples of single variable maximum before that meta thread: math.stackexchange.com/posts/344632/revisions and math.stackexchange.com/posts/116112/revisions Common used as a verb means to put together, right? (Sorry for my English.) Or was it suppose to say the common terms? The main problem I have is that for maximum most were approaching it from a (real) functions angle, but this is just not the only context where it is used. Why not syn it with order-theory? :-) I meant: too common terms Sorry for my typing. You have difficult time with person like me, who is unable to parse an English sentence. Still, there are many questions about finding max-min of a single variable/multivariable function. Having tag for them is not that bad idea. It makes searching easier. But you say that - even without synonyms - (optimization) is not the right tag for such questions. Would you think that separate tag for extrema of real functions would make sense? The objection with order-theory or maximum of finite or countable set are not entirely valid here. I think it is not a good tag, but it's not terrible either. The use of optimazation for that type of question: Find the roots and local extrema of {this function}. Yet, if somebody is searching for the form of a cylindrical can that needs least material and can contain 3 liter of paint and thus searches for the extrema of a function it is reasonably optimization. 1:30 PM The preceding one was an example of an incorrect use - according to what you propose, right? (The one with roots.) Yes. Ok. So basically the new system would be: Extrema for single or multi variable real functions get the new (maxima-minima) tag. And in some cases, optimization fits too - depending on where the problem came from. Is that along the lines what you are suggesting? Yes. But it should have a different name. Ok. I can certainly live with that. I have to admit that now you made to doubt myself - whether I caused the whole maximum -> optimization thing by that meta thread. I still think that I thought such usage before posting it, although I was only able to find very few examples now. The main problem, although I did not articulate this well, is that max min etc is not only used for (real) functions. For example I find this tagging odd. 0 In a problem I am solving, I want to find a quick way or a basic formula to find the nearest integer less than$n$, the problem is stated as follow: Le$n$be a positive integer, and let$x$be a real number. I am searching to find$m$the nearest integer for the formula$x + 2k\pi$($k$... 1:35 PM We cannot see whether it actually came from synonym. Yes. Maybe OP even used optimization. Still it illustrates that IMO optimization is not always a good tag if it is about finding some max or min. OK, as I said I see your point and if a bit of support on meta is shown, I will certainly follow the new guidelines. I guess the problem is still to think of the name of the tag - since you suggest not to use maxima-minima. Perhaps you could cast a downvote on that synonym suggestion, so that it is removed. The thing about tags is that with the number of new tags that appear and with old issues we stumble upon, we could have one tag-related post on meta if we decided to make a post about each one of them. About other issues you mentioned: I made a comment about synonym. In accordance with your "properties are better names than objects", instead of alternative choices could be (separability) - which is too overload - som something like (separability-topology). But I am not sure that is really an issue. My guess is that most people will agree with Brian M. Scott and (countability-axioms) will be removed. I am not sure whether the are some other things you mentioned above, which I skipped. But it is probably better not to discuss too many things at the same time. And I am not sure whether there is much more we can add to either maxima problem or separable problem. 1:51 PM @MartinSleziak I had done that already. Oh. But I still think it is unlikely that it gains 5 upvotes to get to score 4 and get approved. Thanks for the pointer to the digits discussion. Somehow I had missed that one, though it's pretty recent. I think I was quite bust then though. 2014 is not that recent. And (digits) tag was mentioned only as a side note there - it was mainly about representations of numbers in some base. I see no problem with a tag about as long as it is about separable spaces (in general). Ok, I think we both have spent enough time here to start discussing this distinction in more detail. But you can at least see that I remembered your recommendation: "I'd recommend, at least in some cases, not not to name them like the objects." I was looking at what would such tag-name be for separabilty and separabale spaces. If it ends up with separable-spaces, first-countable, second-countable, I think that will be quite good situation. 2:04 PM My concern re separable-spaces and some other things is when a synonym is created that focuses one one aspect of the usage. As long as there is no syn I have no problem with tags being the name of the object. I'll leave no for a while. Thanks for the discussion. Thanks to you as well - both for your time and for your insights. 1 hour later… 3:26 PM @MartinSleziak sorry to come back to this tangential detail but it was this September, September 14th to be precise. Maybe you read it as September 2014, which would be more logical as far as I am concerned, yet not intended. The tag is a mess. @quid My mistake. And you are right, I saw 14 there and thought it was 2014. There are probably many tags which are in a bad state. I usually post here new posts from tag management thread. So I should do that for you post about existing$\to\$ synonym and relation to too:
0

The tag digits is a synonym of decimal-expansion. I think this is not good as it leads to questions that are not at all about decimal expansion to be tagged as such. Instead this tag should likely be a synonym of number-systems, in any case the synonym should be removed (or maybe reversed). ...

Although usually there are only a few posts per day, so if somebody peeks here, they notice the linked post right away. Like here chat.stackexchange.com/transcript/3740/2016/12/2 or chat.stackexchange.com/transcript/3740/2016/11/30 I guess today was different.
But it is good to see that there are people who care about tags.
And also on meta Alex M. posted a few tag-related questions recently, and perhaps some other user, who I cannot remember right now.

4 hours later…
7:53 PM
0

There are separate tag connectedness and path-connected. In the tag-info cor connectedness it is explicitly mentioned that it includes (among other thing) questions about path-connectedness. (Moreover, having too many closely related tags causes problem, since there is a limit at most 5 tags per ...

yesterday, by Martin Sleziak
There are some questions which use (countability-axioms) tag simply as: "Well, do we have some tag about countable sets? This seems like that." They should be retagged no matter what the outcome of the discussion on meta is. The questions tagged countability-axiom but not general-topology are natural suspects.
I still might have missed a few, but after the clean-up, the tag is down to 31 questions.