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Two days ago I asked a question about some notation that I did not understand in a textbook. Yesterday I sat down for a while and slowly worked through the proof while trying out some of my 'best guesses' at what the notation meant, and I discovered that the guess that I had made in the original question was correct (everything worked out in the end!).

I self-answered and received several delete-votes.

In this situation, would the better response after figuring out my confusion to have been to delete my question? Or, what changes can I make to make my answer more acceptable for this site?

Note: This meta post asks about a very similar situation, but my question ended up being a rather simple yes/no: "is my guess correct?", and I am wondering in this particular case if my self-answer is (or could be made) useful, or if it is instead just adding clutter to the site.

I got the feedback from one user that

IMHO, your question is limited to yourself and not helpful (or maybe) for broader audience.

Update: The user first expanded on their one-line self-answer, but soon decided to delete the Question (and thus the Answer as well).

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    $\begingroup$ @ArcticChar I haven't gotten downvotes, but I got 3 votes to delete my answer in the review. math.stackexchange.com/review/low-quality-posts/1437750 And while in the end it was not deleted, I would like to know how to improve or better-handle my case of question/answer $\endgroup$
    – Air Conditioner
    Aug 15, 2020 at 15:14
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    $\begingroup$ There is nothing in principle wrong with posting a self-answer in the circumstances you outline here. However the standards for Answers are stricter than they are for Questions, since Answers are expected to be definitive conclusions. Rather than voting to delete, I'd hope to give constructive criticism on your post. Certainly one-line Answer posts are likely to automatically appear in the Low Quality Post review queue. $\endgroup$
    – hardmath
    Aug 15, 2020 at 15:18
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    $\begingroup$ I do not agree with the quote at the end that your question is not helpful. But I would agree to that if the term "question" is changed to "answer". $\endgroup$
    – Arctic Char
    Aug 15, 2020 at 15:21
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    $\begingroup$ Also, if you haven't faced this yet, if you delete questions multiple times(with or without negative or positive rating), the system flags you and might even put a soft question ban....In my case, i didn't even have criticism, just supposedly targeted votes, and ya... i deleted my post think it will not have an effect on me(NOT ON MATHSE) $\endgroup$
    – Anindya Prithvi
    Aug 15, 2020 at 15:33
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    $\begingroup$ I disagree that the question is "limited to yourself and not helpful (or maybe) for broader audience". Such an attitude seems dismissive of all questions of the form "I was reading this in a book and I don't understand it!", but such questions are surely helpful to many readers of those books (which is potentially a larger audience than most of the questions here!). $\endgroup$
    – user1729
    Aug 15, 2020 at 21:47

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I disagree that this is only a simple yes/no question. Well the ultimate answer is either yes or no, but you do need justifications. Think, for example, if some user posted another answer saying

"No, the “cosets” in his notation are not the orbits under the right-action of $H$"

Then what should we do? How can we judge which answer is correct?

In general, to constitute a good answer in MSE, the claim has to be supported by mathematical reasoning. Just the same way you come to the conclusion in this particular doubt.

I suggest the following: you said you "slowly worked through the proof while trying out some of my 'best guesses' at what the notation meant". Put that into your answer. Explain how you come to this conclusion.

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    $\begingroup$ One might expect of a self-answer that the OP, having been confused on the very point of arriving at the conclusion, would have a special insight into what makes it correct and some effort to explicate this will be more likely to benefit a future Reader than the bare conclusion. $\endgroup$
    – hardmath
    Aug 15, 2020 at 15:23
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    $\begingroup$ Hmm, my conclusion was primarily reached by having slightly more wakefulness and willpower to copy and parse through categorical things sentence-by-sentence. I sometimes feel reluctant to proceed further when there is word-choice and definitions that I am not sure of, and want to confirm that my understanding of these things is correct before doing much more reading (because it can lead to a lot of wasted time (and even more confusion) in the end if said assumptions end up being incorrect). I'll think a bit more on whether there were any big insights that occurred, but I'm not sure there are. $\endgroup$
    – Air Conditioner
    Aug 15, 2020 at 15:37
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    $\begingroup$ If you end up not writing up the details (for whatever reasons), please consider deleting that answer. For the question itself, it's up to you. Some might come and give a great answer (e.g. point out exactly which page May had given the definition) @AirConditioner $\endgroup$
    – Arctic Char
    Aug 15, 2020 at 15:42
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    $\begingroup$ @ArcticChar Thank you for all your advice so far. I added in a list of the things that 'worked out' properly under the substitution of 'orbit' for 'coset'; is this any improvement? $\endgroup$
    – Air Conditioner
    Aug 15, 2020 at 16:19
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    $\begingroup$ @AirConditioner From your new edit : if that had been your original answer prior to downvoting and deletion, you may have had better reception! Remember this : an answer to your question should not be sufficient to meet your own demands just because it is your question : it is as good as public property once you post it, so the answer must also be similar. However, I suppose this is a learning curve, and you will get better as you go. +1 for asking this question. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Aug 16, 2020 at 6:13

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