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In the following questions:

Prove that for all real numbers $a$ and $b$, $|a|\leq b$ iff $-b\leq a\leq b$.

Prove that $B\cup(\bigcap \mathcal F)=\bigcap_{A\in \mathcal F}(B\cup A)$.

the answers provided by J. W. Tanner and Brian M. Scott respectively were extremely helpful and after thinking a lot about their answers I gained a new perspective into the mechanics of proof writing $($which currently I am self learning$)$.

Is it a good idea to add those perspectives and explain the root of my mistakes and confusions in the body of the question in form of an edit$?$ Such that it might help future readers$?$

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    $\begingroup$ No. It is not a good idea, after others have already answered your question, to modify your question, in such a way that their answer no longer makes sense. $\endgroup$ – amWhy Jul 18 '20 at 17:02
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    $\begingroup$ I did not mean to edit the original post beyond recognition but simply to add one to the original post. $\endgroup$ – Khashayar Baghizadeh Jul 18 '20 at 17:21
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    $\begingroup$ And... in so doing, make one of the original posts appear pointless, because, by editing to include the original post, you'd be rendering that original post a copy of what your "edited post" then states. $\endgroup$ – amWhy Jul 18 '20 at 17:30
  • $\begingroup$ @amWhy Thank you. $\endgroup$ – Khashayar Baghizadeh Jul 18 '20 at 18:20
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    $\begingroup$ @KhashayarBaghizadeh Lovely question, and I hope answers were satisfactory. +1. The root of your mistakes and answers, were pointed out by those answering your question, so not editing your post gives respect to the originality of those answers. Don't worry, future readers who want material will pick it up from where they need to : the answer. $\endgroup$ – Teresa Lisbon Jul 28 '20 at 6:36
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Remember, if you change your existing post too much some of the answers may become confusing if they address points that are no longer there or are stated differently. So don't edit your question just to remove a mistake — we all make them and others can learn from yours if you leave them up.

If you want to add a note to your question, you can draw a horizontal line and write "Edited to add: I now realize ...". But remember, this isn't a class where you have to demonstrate to your teacher that you have internalized the answer; do so only if it would be helpful to future readers. For instance, when I glance at your first linked question, there is one short answer that is top-voted and accepted. Future readers can read your question and that answer, and get a complete picture. They are unlikely to gain anything from you repeating the answer as an edit to your question, and sometimes edits like this can make the flow of ideas harder to follow. So I wouldn't bother there.

It takes a while to change from writing up math for homework to producing posts that best help future readers, so thank you for asking about this and being considerate of how others use the site.

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  • $\begingroup$ Thanks for the guidance. $\endgroup$ – Khashayar Baghizadeh Jul 18 '20 at 12:28
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    $\begingroup$ Surely. But I'll suggest you remove the "Accept" checkmark for now. I've only been here three years, and you may get other answers with different or better insights if you leave the question open. $\endgroup$ – JonathanZ supports MonicaC Jul 18 '20 at 12:33
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    $\begingroup$ @JonathanZsupportsMonicaC If a user has been immensely helped, and says so in a meta post, by answers from posts they've accepted, I don't think it's your place to suggest they remove the "Accept". Better advice would be to not, in the future, feel pressured to accept an answer if you are not completely satisfied. $\endgroup$ – amWhy Jul 18 '20 at 17:06
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    $\begingroup$ @amWhy: I think there's some confusion. Khashayar had give this answer of mine an "Accept" after their question had been up only a little while, and, as I said, I'm not super experienced around here, plus it was pretty early in the U.S., where a lot of users are. So I thought this Meta question could benefit from some more time open and some more answers. The "Accept" checkmark I advised removing was the one on this answer. $\endgroup$ – JonathanZ supports MonicaC Jul 18 '20 at 19:06
  • $\begingroup$ Thanks for the explaination, @JonathanZsupportsMonicaC. I respect your decision here. $\endgroup$ – amWhy Jul 18 '20 at 19:13
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I think it would be a good idea to post what you've learned as an answer to your question, rather than as an edit to the question. (Of course, if you do that, then you should phrase it in the form of an answer to the question.)

In particular, suppose that you post a problem, somebody else posts an answer containing some information, and you use that information to come up with a complete solution to the problem. Then it would be a very good idea to post that complete solution as an answer to your own question, and in your answer post, you can certainly explain why you were confused in the first place and what insights you gained from the other person's answer. (And of course, you should make sure to give credit to the person who posted the helpful answer; don't make it sound like you came up with the solution yourself independently of what they posted.)

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For future readers, in an ideal post of the site, one should be able to immediately identify the mathematical statement, or the essence of the question when the soft-question tag is used. It is the "question-and-answer" part in the post that most of the potential readers would care about.

It is OK to add the "gained perspective" into your post as long as it is of reasonable length and does not change the original question. Though, it may add extra unnecessary noise to the existent post unless they are some deep insights.

Is it a good idea to add those perspectives and explain the root of my mistakes and confusion in the body of the question in the form of an edit? Such that it might help future readers?

In a solution-verification type question, "the root of my mistakes and confusion" is supposed to be explained in an answer. Adding those to the original question may be redundant.

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