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This question was recently deleted (with 3 users voting to delete). The help topic "why and how are some questions deleted" says questions are deleted if they are "extremely off topic" or "very low quality". "Extremely off topic" certainly does not apply to the question. Not sure what "very low quality" means. I think it means a question asking users to answer a homework problem without any description of the things the asker doesn't understand. I certainly don't see how "very low quality" could apply to this question. The question is short, but it is something that many people have probably asked themselves when studying Riemann integrals.

In that help topic, it also says that "the number of delete votes required scales to the number of votes on the question and all its answers". There were at least 14 positive votes on the answers to this question before it was deleted.

So how could this question be deleted?

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    $\begingroup$ The question had score zero, the top-voted answer has score 6. If I understand correctly the details of the deletion votes, the sum of these two scores has to be at least 20 for the question to require more than 3 votes to be deleted. Here is the post which is linke in the FAQ: Should delete votes be limited like close votes? $\endgroup$ – Martin Sleziak Jul 7 at 17:47
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    $\begingroup$ @MartinSleziak: It seems that the question has net score 1: webcache.googleusercontent.com/… Perhaps the version I can see from Google cache is old. $\endgroup$ – T. S Jul 7 at 21:35
  • $\begingroup$ @T.S 10k+ users can still see deleted questions. So if you have somebody around, you can ask them to confirm what the scores are currently. Or you can wait until the next update of data in SEDE and you can check for yourself what is the score of the question and of the answers. $\endgroup$ – Martin Sleziak Jul 8 at 3:00
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How could this question be deleted?

Quoting from this answer on the main meta site (with a tip of the hat to Martin Sleziak):

We had discussed this before, but deferred until there was a problem - it seems we now have a problem :)

The new rules (also apply to undelete votes):

  • 10k rep users get 5 deletion votes per day on questions they don't own, increasing by 1 vote per extra 1,000 reputation up to 30 votes per day - deletion rules on questions one does own are still in effect.
  • Popular questions require more deletion votes to be deleted, at a ratio of 20:1 - a question's popularity is defined as: question score + top-scored answer score. For example, a question with (question score 15 + top answer score 5 = 20) will require 4 deletion votes (3 base votes + 1 popularity vote).
  • The maximum number of delete votes needed will not exceed 10.

Note that the above rules apply only to questions; answers take 3 votes, regardless of score.

At the time that this question was deleted, it had a net score of $0$, and the top answer (which was written by J. Heller) had a net score of $+6$. This gives that question a "popularity" of $6$, which is well shy of the threshold required for an additional delete vote. Therefore, from a purely mechanical point of view, the answer to the question "How could this question be deleted?" is that

  1. five users felt that the question failed to meet the quality standards of the site and voted to close it, and
  2. the question was insufficiently popular to require more than three delete votes, and three users voted to delete it.

However, I believe that the asker of this meta question is also interested in the following:

Why was this question deleted?

While the asker of this meta question does not explicitly ask why the question was deleted, it seems implicit form the phrasing of the question that this is also of concern. The question was closed for lacking context. The canned close reason reads

Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc.

Thus those who voted to close the question (including myself) felt that it did not meet the consensus standards for quality. The asker of this meta question asserts that "The question is short, but it is something that many people have probably asked themselves when studying Riemann integrals." I do not disagree with that statement, but I see nothing in the meta-thread on asking a question which indicates that a question being common, on its own, is sufficient to justify retaining that question on this website.

While one can read the close reason and the "how to ask a good question" thread, it might be helpful to elucidate specific concerns about the question being discussed here.

  • Strike one against the question is that the actual question is in the title only, and not contained anywhere in the body of the question. This makes the question less accessible to mobile readers. However, this is not a big deal, and can be easily fixed.

  • More importantly, the question lacks much in the way of context. In this case, the asker has two bits of notation, $$ \lim_{n\to\infty} \left( \sum_{i=1}^{n} x_i \right) \qquad\text{and}\qquad \sum_{i=1}^{\infty} x_i, $$ and wants to know how they differ. However, the asker doesn't actually explain what either piece of notation means. The first is, arguably, clear. However, the second really does require some explanation. In most elementary texts with which I am familiar, the definition is something like

    Definition: Let $(x_i)_{i=1}^{\infty}$ be a sequence, and suppose that the sequence $(S_n)$ converges to $S$, where $S_n$ is defined to be $$ S_n = \sum_{i=1}^{n} x_i. $$ Then define $$ \sum_{i=1}^{\infty} x_i = S. $$

    From such a definition, the distinction between the two notations is immediately clear (i.e. the infinite series is only defined if the limit of the partial sums exists). Of course, other texts may have slightly different definitions, so it is incumbent upon the asker to explain what the notation is meant to mean. Something like this was communicated to the asker by this comment, which was posted several days before the question was closed (hence the asker had time to add context to their question).

  • Finally, I think that the question is unclear. Specifically, I find the reference to Riemann integration a little confusing in this context. Ideally, the asker would provide some context for that comment by giving an example. More generally, if one encounters notation which is confusing, then one should give one (or more!) example(s) of the notation being used. If they are confused about the notation being used in the context of a Riemann sum or integral, then they should specifically spell out an example in which this confusion is made manifest.

    Moreover, as has been pointed out in the comments below, the question has five answers, three of which ([1],[2],[3]) seem to have a common interpretation of the question, and the other two of which seem to have distinct interpretations ([4],[5]). The fact that the answerers cannot agree on the correct interpretation of the question is, to me, evidence that the question is unclear.

Other close-voters may have additional reasons for believing that the question fails to meet the quality standards of the site. In any event, the question was closed, and the close reason is, essentially, that the question is of low quality.

Once a question has been closed, it is eligible for deletion. I would argue that if question is closed then, after a certain amount of time, the question ought to be deleted unless there is a compelling reason to keep it on the cite. Compelling reasons might include the following:

  1. The asker (or someone else) improves the question so that it meets the site's guidelines, in which case the question should be reopened.

  2. The question is closed as a duplicate, but is otherwise of high quality (such questions can serve as roadsigns for future askers).

  3. The question has historic or cultural significance for this site (my go-to example of such a question is the Batman question, which is hardly even a question; the question and its answers, however, received thousands of upvotes and hundreds of thousands of pageviews, so there may be some reason to keep it around).

  4. The question has attracted a truly stellar answer. In general, I feel that questions should be judged in isolation. However, sometimes a very poor question attracts a phenomenally good answer. In such cases, it may be worth keeping the question around in order to preserve the answer. I would argue that such cases are quite rare, and that a better solution is to ask a new version of the question, then ask the moderators to merge the old question with the new, improved question.

This list is likely not exhaustive, but it should give a sense of when not to delete a question. In the current situation, the question was closed for lacking context (i.e. it was closed because it was considered to be of low-quality), and was not subsequently improved. As the question is not of historical significance to the site, nor are any of the answers particularly exceptional, the question was deleted.

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    $\begingroup$ What kind of "context" do you see in this question you answered several days ago? And notably this 2019 one? They are all similar notation questions. How do you determine whether a question "is of historical significance to the site" or not?? $\endgroup$ – T. S Jul 7 at 22:03
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    $\begingroup$ @T.S this type of "calling out" based on past (answering) activities is not appropriate. If you truly want to ask if or what difference Xander sees please frame it like that and not in a way that is hard not to read as an accusation. $\endgroup$ – quid Jul 7 at 23:52
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    $\begingroup$ I disagree that the question lacked context. The asker wanted to know the difference between two notations in the context of the Riemann integral. The simplest definition of the Riemann integral is $\int_a^b f(x) \,dx = \lim_{n\rightarrow\infty} \sum_{i=1}^n \frac{b-a}{n} f(a+i(b-a)/n).$ It is clear that the asker wanted to know why this cannot be written as $\sum_{i=1}^{\infty} \frac{(b-a)}{n} f(a+i(b-a)/n)$. $\endgroup$ – J. Heller Jul 7 at 23:55
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    $\begingroup$ @J.Heller until you said it that was not clear to me. And it visibly was not clear to most users that answered the questions either. It is actually a good guess of what the user likely meant to ask but if anything it shows that it did lack context, because 3 out of 4 users that answered the question did not address that at all. $\endgroup$ – quid Jul 8 at 0:02
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    $\begingroup$ @quid: if you don't want to be neural as a moderator should really be, then please save it and don't ping me. I see no problem whatsoever in my comment. The questions I linked, all answered by Xander are similar to the one said by OP. They do share the same tag notation. The "is not of historical significance to the site" judgment completely contradicts what Xander's opinion of "historical significance". $\endgroup$ – T. S Jul 8 at 1:13
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    $\begingroup$ @T.S it is not unexpected that you see no problem with your comment. It is often the case that we are not the best judges of our own doings. As I explained, if you want to ask Xander what if any difference they see that is fine. If the point of your comment is merely, and the follow up suggests this, to point out that Xander has answered arguably similar questions in the past then this is inappropriate and besides the point. $\endgroup$ – quid Jul 8 at 1:29
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    $\begingroup$ @T.S Regarding the two questions to which you have linked, I would be happy to chat with you about them. However, they are not relevant to the discussion of the question linked here. Regarding historical significance, I am not sure what your point is. I have asserted that the "Batman question" has been preserved for reasons of historical significance. This particular reason for preservation is not one which I would apply to any other question which has been discussed in this thread. $\endgroup$ – Xander Henderson Jul 8 at 2:18
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    $\begingroup$ @T.S I swear some users do not have a hint of self-awareness. "My subjective opinion is objective reality!" gets thrown around here quite a bit. Also, "Here are a handful of examples of why I'm right! ... How dare you challenge my examples/your counterexamples do not apply!" And the tone policing, haha. Remind me of the RAs at the university I went to. $\endgroup$ – user762914 Jul 8 at 3:02
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    $\begingroup$ @user762914 I hope the irony of you saying that in reply to a comment that says "I see no problem whatsoever in my comment." and considers that the end of the discussion, is not lost on you. :-) $\endgroup$ – quid Jul 8 at 12:41
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It is straightforward, actually. There's a group that congregates in the CURED chat (https://chat.stackexchange.com/rooms/2165/cured) that publicize questions they don't like to one another. They then collude to downvote and close questions.

Here's Saad at 5:12 pm, pointing them to the question you asked about:

For closure: 3747194 For deletion: 3740512 3734926

They are fighting the good fight or something like that.

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    $\begingroup$ C'mon downvoters, just be honest. This isn't a democracy or kindergarten classroom. Some opinions are worth more than others, and they decide the content on the site. Stop hiding behind procedure and the myth of arbitrary and independent review of questions, when the answer is much simpler: there's some kinds of content you don't want around, and you have the power to implement that vision. Just say it, you'll feel better, and people will stop arguing with you about the "facts" or "context." $\endgroup$ – user762914 Jul 8 at 3:12
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    $\begingroup$ I'm genuinely curious, given the tone of your answer and your comment: what's your contribution here? Are you just sniping from the sidelines, trying to make everyone a little more miserable, or are you participating in CRUDE, GENTLE and the like and trying to make a difference? $\endgroup$ – postmortes Jul 8 at 5:25
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    $\begingroup$ @postmortes I am not trying to make everyone a little more miserable. My opinion is that the site is not designed to achieve the goals that many people want, and this leads to lots of misunderstanding and frustration with people who are just going about their business, like the OP. To the extent I make a difference, it's by engaging with people who ask questions and taking them as they are, as individuals with different mathematical and linguistic capacities and needs. I find elitism and gatekeeping tedious. I hope I forget about the meta in a few days and you will never hear from me again. $\endgroup$ – user762914 Jul 8 at 5:50
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    $\begingroup$ Thank-you :) When you say that the site is not designed to achieve the goals that many people want this seems to exclude the possibility that people are not using the site for what is was designed. Is it possible that what you're describing as elitism and gatekeeping is actually people trying to keep the site for what it was designed against people who want to change it for their own ends? It seems that either point of view would be unnecessarily polarising (to me) $\endgroup$ – postmortes Jul 8 at 5:55
  • $\begingroup$ @postmortes I don't know that there is like, a conspiracy of undergrads out there trying to turn the site to crap. I think a lot of people are turning to this site for math help right now, particularly because of the covid, and they're told to learn latex and give more context because their question sucks. I find that sad. Anything is possible, but I'm not killing off other people's questions and answers. I don't think it makes sense to put a site on the internet for people studying math and then treat neophytes and the people who try to help them like a nuisance. $\endgroup$ – user762914 Jul 8 at 6:05
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    $\begingroup$ That's a reasonable point, definitely. However... this isn't a site to help people study math -- there are other sites whose aim is explicitly that (I think Khan Academy is one such). This is a reference site: you have a question, you look up an answer, like an online textbook. The only difference to the textbook is that if your question doesn't have an answer, you can ask it anyway and maybe the answer will be added. (The chatrooms can be used to get a more teacher-student experience, but they're not archived permanently, or searchable, I think.) $\endgroup$ – postmortes Jul 8 at 6:10
  • $\begingroup$ @postmortes I will forget about the meta and stop bothering the superusers. I just made the mistake of clicking on a meta question link and now people are @'ing me and it brings me back here and I have lost my mind. I think the concept of a reference site is fine, but the quality control is backwards: you should let the people who are really into the concept of a reference site decide what goes in the archive and consolidate it after it is finalized, not have them crush the people asking question and offering answers. That is how you get OP's post and people like me. $\endgroup$ – user762914 Jul 8 at 6:13
  • $\begingroup$ @postmortes I am not trying to change your mind or anything, though, the character limit just doesn't allow nuance. I hope you enjoy the site and look up many useful things. $\endgroup$ – user762914 Jul 8 at 6:15
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    $\begingroup$ Sorry to ping you again; this will be last time :) What you described in your second-to-last comment is exactly what is happening, and what OP is complaining about: the question they chose to answer hasn't been selected for archival after it's been reviewed. We appear to be on much the same page :) $\endgroup$ – postmortes Jul 8 at 6:17
  • $\begingroup$ @postmortes The searchable archive and what exists at the site do not need to be the same thing. The OP and the asker collaborated with other people on something and it has been destroyed. The asker no longer has any access to it, nor the OP. I have no idea what they are even talking about, I just see "page deleted", which could happen for a variety of reasons. This is adjacent to a larger debate over how the site should not be tolerating "low quality" questions and "low effort" contributions. For coding, I understand it all, but for math, I don't. $\endgroup$ – user762914 Jul 8 at 6:24
  • $\begingroup$ @user762914 Thanks for your thoughtful comments here. After this, I must conclude that this site has a bad design. There are far too many hoops to jump through just to ask or answer a simple question. In a properly designed site, there would be no such hoops. I would prefer a site that is simply a community of people of all levels of knowledge freely sharing their knowledge. $\endgroup$ – J. Heller Jul 8 at 16:39

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