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Below I quote an answer that I posted. It was deleted. I do not know which users deleted it, so I cannot ask them what objections they had to it.

Does anyone know a reason why such a thing ought to be deleted?

If those who deleted it see this, can they tell me what they objected to? If I knew that, then I would know whether I agree with the objections, and if I found merit in them, I could have edited the posting before it was deleted, or I could take that information into account in future postings.

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Two points:

  • In some commonplace metric spaces such as $\ell^2,$ there are sets that are closed and bounded but NOT compact. In particular, the standard orthonormal basis of $\ell^2$ is an example of such a set. And the closed interval from $0$ to $1$ within the space of rational numbers with the usual metric is another example. These examples are closed and bounded but not compact.

  • Mathematicians have long been trapped within a general way of doing mathematics that tacitly encourages NOT motivating definitions. The definition of a "group", for example, is motivated by the fact that many concrete example have certain things in common. But textbooks say: "DEFINITION: A group is etc.etc.etc." It's dogma. Mathematics should be done non-dogmatically, and in some respects it is.

    And here I will make a bolder claim: The pattern of thinking that results in this dogmatism among people who think their subject is done non-dogmatically is the SAME thing that causes required math courses in schools to in effect be taught dogmatically, by a mechanism that works in front of everybody's faces, except that they never look in that direction.

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    $\begingroup$ Here is a link to the answer. You have more than sufficient reputation to see this link, and could recover it yourself by looking at the recently deleted answers section of your profile. $\endgroup$
    – Xander Henderson Mod
    Sep 5 '20 at 0:06
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    $\begingroup$ @XanderHenderson : I attempted to find this and could not even find the question. That there is such a thing as a recently deleted answers section of a profile is news to me. $\endgroup$ Sep 5 '20 at 1:32
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    $\begingroup$ @MichaelHardy math.meta.stackexchange.com/questions/13948/… $\endgroup$
    – Xander Henderson Mod
    Sep 5 '20 at 13:53
  • $\begingroup$ Typical grounds to delete an answer are that first three users, for low to moderately voted answers, who have the reputation to vote to delete, do so, and to redelete, that three users with the reputation to delete an answer, do so. $\endgroup$
    – amWhy
    Sep 5 '20 at 22:12
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    $\begingroup$ @MichaelHardy In the last couple of days, you have asked two questions on meta: this one, and the dupe target. Both questions appear to be asking essentially the same thing: who voted to delete my answers, and why? Because they both appeared to be addressing the same underlying issue, I closed this one as a duplicate of the other. $\endgroup$
    – Xander Henderson Mod
    Sep 6 '20 at 17:22
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    $\begingroup$ That being said, I am perfectly happy to reverse the direction of the dupe-closure, given that this question is more specific than the previous question, and it appears that both questions were motivated by the deletion of the same answer. $\endgroup$
    – Xander Henderson Mod
    Sep 6 '20 at 17:28
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I will note that this answer is given in my capacity as a general user of the site, and not as a moderator. This answer does not express any official policy or consensus of the moderation team.

There seem to be three questions being asked here:

  1. Can I see who voted to delete my question?

    It depends. Before a post has been deleted, the number of deletion votes will be shown, but not the identities of those that cast the votes. After a post is deleted, the identities of those that cast delete votes will be shown in a banner above the post, which will remain visible to those users with enough reputation to see the post. Taking the question which motivated this discussion as an example:

    enter image description here

    Note that deleted posts can be a little more difficult to find, as they are not displayed on the mainpage or via the SE search tools. However, recently deleted posts can be found by the authors of those posts. For more details, please refer to the meta question "Is there any way to see my deleted questions or answers?"

  2. May I ask those that voted to delete why they did so?

    Generally speaking, no, you may not. One cannot comment on a deleted post, and it is considered somewhat rude to ping users by responding to unrelated posts. I would suggest that the best strategy for dealing with deleted posts is to simply move on. I understand and appreciate the desire to know what one can do to improve one's posts, but, more often than not, discussions about why a post was closed or deleted lead nowhere, but produce a lot of acrimony and hurt feelings.

    Alternatively, you can request that a question be undeleted via the Requests for Reopen & Undeletion Votes (volume 07/2018 - today) thread. Once a post has been undeleted, you can ask for feedback.

  3. Why was this answer deleted?

    I don't know.

    If I might speculate, it is because the answer doesn't really address the question at all. The first paragraph gives an example of a metric space which possesses closed and bounded subsets which are not compact. The question is about why the definition of compactness is the way it is isn't addressed at all by this paragraph.

    The next two paragraphs aren't really even about mathematics. They make debatable assertions about the dogmatism of mathematicians, but don't seek to provide answers to questions they raise about interrogating the motivation behind definitions. In particular, you assert that "Mathematicians have long been trapped within a general way of doing mathematics that tacitly encourages NOT motivating definitions," but you fail to provide motivation for the definition of compactness, which is what the original question is about.

    For the record, I entirely agree that definitions should be motivated, and that students should be asked to interrogate the motivation behind definitions—this is a large component of courses which I teach, including some very introductory level classes. Unfortunately, this is beside the point, as the question wasn't about pedagogy. It was a specific question asking for clarification regarding a specific definition.

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  • $\begingroup$ How do you feel about partial answers, addressing some but not all of what was asked? "the answer doesn't really address the question at all" but it does say why "compact" is not defined as "closed and bounded", and that was explicitly asked. $\endgroup$ Sep 6 '20 at 19:27
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    $\begingroup$ @MichaelHardy I gave you my opinion. If you are sincere in your desire to understand why people may have voted to delete your answer, then please do with my opinion as you desire (either edit your answer, or ignore me). I am not going to engage in a long comment thread about this, as (quoting my answer above) "more often than not, discussions about why a post was closed or deleted lead nowhere, but produce a lot of acrimony and hurt feelings." $\endgroup$
    – Xander Henderson Mod
    Sep 6 '20 at 19:32
  • $\begingroup$ +1 for last paragraph about motivation behind definitions. Maybe such things should be made mandatory for textbooks as it would turn out to be a boon for those engaged in self-study. $\endgroup$ Sep 7 '20 at 7:13
  • $\begingroup$ it is considered somewhat rude to ping users by responding to unrelated posts --- Ooops! However, in this case I was a bit irritated so the possibility of coming across as somewhat rude does not bother me. $\endgroup$ Sep 7 '20 at 17:44
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    $\begingroup$ @DaveL.Renfro That is actually a case where you should raise a flag. Generally speaking, it is not okay for an answerer to delete their question after they get an answer. This indicates disrespect towards the answerer who provided an answers, disrespect towards other potential answerers, disrespect towards future readers who will be deprived fo quality answers, and is also sometimes a way in which people try to cover their tracks while cheating. Again, if you see it happen, please raise a flag. $\endgroup$
    – Xander Henderson Mod
    Sep 7 '20 at 17:53
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    $\begingroup$ In that particular case, the question is a month old, so I think it is a little too late to take action. But it is something to keep in mind for the future. $\endgroup$
    – Xander Henderson Mod
    Sep 7 '20 at 17:55

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