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The purpose of this thread is to help focus the attention of the community on posts that may require reopen and undeletion votes. A request should be posted as an answer below (one request per answer).

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Earlier versions of this thread that served as a model:

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    $\begingroup$ I edited the post inspired by a concern expressed in a comment. $\endgroup$ – quid Jul 19 at 23:49

182 Answers 182

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Reopened

I would like to see this question reopened. It is certainly not a duplicate of the previous question as here a double sum have to be evaluated. A partial answer ("the inner sum") which was considered in a comment as "promising" is in fact not helpful at all.

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Undeleted

How to undelete the following question $\sum_{i=1}^n ( nGx_i^{G} + G^{x_i}) \ge n^2G + G^2n$, for all $x_i>0$, where $G=\prod_{j=1}^nx_j$.

As you see, some users have done serious contributions in order to solve the conjectured problem, so it may be unfair to permanently delete the whole discussion. My own attempts to solve the questions were fruitless.

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Reopened

I tried my best to edit this question to make it more concise, if anyone has recommendations on how to make it even better pls just ping me

Why do sometimes care for where vectors originate from and sometimes not? and exactly how many kinds of vectors are there?

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Undeleted

May I request that this old question Countably Infinitely Many Points in a Euclidean Space of mine be undeleted? The deletion was done by an automatic system (if that is the case, can it be voted to be undeleted?). I am certain that the question is well written with a lot of context. I would like to put a bounty on the question.

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I request that my question here is reopened:

Do I understand the difference between $\implies$ and $\to$?

I ask some very specific questions about the use of $\implies$ and $\to$ that it is different from the duplicate question.

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  • $\begingroup$ I suspect it would help your case if you edited your question to remove anything covered by the linked question, and also to made clear the differences between your question and the linked one (whilst still making the question readable, etc.). This would make it easier for people to judge the differences. $\endgroup$ – user1729 Sep 1 at 9:15
  • $\begingroup$ @user1729: I can do that. I just wanted to give the context that I was working in. $\endgroup$ – John Doe Sep 1 at 13:41
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Locked, Unlocked

Please reopen this thread: Given $n$ integers $p_0, p_1,...,p_{n-1}$, what is the smallest possible degree of a polynomial $p(x)$ such that $p(i) = p_i$?. I answered it (although it is now a community wiki post), but the thread is very much self-answered.

I think the thread is useful. There are many questions of the form: "Given a part of a sequence $a_0,a_1,a_2,\ldots,a_{n-1}$, determine the value of $a_m$ for some integer $m\geq n$." I personally dislike such questions because the given information is not sufficient, but with the added assumption that the sequence is a polynomial sequence (of degree at most $n-1$), then such questions become answerable, and we can use some idea from the thread above to establish answers to such questions.

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    $\begingroup$ Interesting to see a moderator joining an edit war... $\endgroup$ – Arctic Char Sep 4 at 17:29
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    $\begingroup$ @ArcticChar That is why I think the moderator's actions were inappropriate (whence the complaint in Math Mods' Office). $\endgroup$ – Batominovski Sep 4 at 17:44
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Reopened and Undeleted, Closed again, Deleted, Undeleted, Deleted again

I think the following question should be reopened: What Are The Elements of $e$ in Set Theory?

It is an intriguing question which is no less deserving of attention than many of the questions we get here (I'd rather this kind of conceptual question than yet another integral to solve). It seems to me that the issue with the question is that it is not well-posed (to quote Asaf's answer, the answer "depends on which set is $e$"). However, the answers are explain the issue with the question and how to resolve it, which is the kind of answer I think the question needs.

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    $\begingroup$ Maybe the question is not that bad as it has elicited nice responses from various well established users. But the asker is not really keen on learning from the responses, and perhaps not really clear about their purpose in asking the question. It should be closed as "needs clarity". If the questions includes some proper context about definition of $e$ as well as its representation then it is more likely a candidate for reopening. $\endgroup$ – Paramanand Singh Sep 1 at 12:04
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    $\begingroup$ @ParamanandSingh I disagree. It is clear that their purpose is that they wished to understand a comment of Asaf from elsewhere. One of the key points in the answers, and one of the subtleties of the question is that it matters how we define $\mathbb{R}$, so asking the OP to clarify this undermines this. Also, I don't think we should be judging the question based on the user, or their comments to the question; indeed, if we ignore the comments then everything is nice. $\endgroup$ – user1729 Sep 1 at 12:50
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    $\begingroup$ I am not judging users, the question does require a bit more clarity, for example what particular definition of reals is being used. A link to Asaf's comment on which this is based should also be included. Is the asker familiar with the set theoretic development of number systems or not? $\endgroup$ – Paramanand Singh Sep 1 at 15:06
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    $\begingroup$ Had these points been included in the question I think it would have been received very differently. $\endgroup$ – Paramanand Singh Sep 1 at 15:10
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    $\begingroup$ It is hard to believe the question is honest given the comments left in some of the answers. $\endgroup$ – Andrés E. Caicedo Sep 14 at 19:53
  • $\begingroup$ @AndrésE.Caicedo I don't think we should be judging the question based on the user (who has a reputation for crankery), or their comments to the question; indeed, if we ignore the comments then everything is nice. $\endgroup$ – user1729 Sep 14 at 20:39
  • $\begingroup$ @ParamanandSingh I learned from the responses that there exists more than one possibility for the elements of e, and it's cardinality. I didn't realize that before I had asked the question. I asked about how they could all represent the same set, since once set doesn't have two cardinalities. I didn't get a response to that, and one person apparently wanted no learning about the cardinality of e. Perhaps my incorrect assumption was that there was one unique set theory, when there exist multiple set theories with conflicting concepts of e. $\endgroup$ – Doug Spoonwood Sep 15 at 13:29
  • $\begingroup$ @DougSpoonwood: I am not an expert on set theory so can't really say much here. Perhaps you should add all such clarification as a part of your question. $\endgroup$ – Paramanand Singh Sep 15 at 14:12
  • $\begingroup$ @DougSpoonwood The point is that the "cardinality of $e$" doesn't matter, because its elements however you define is as a set mean different things depending on the definition. If you define it as a Dedekind cut, it is the set of all rationals less than $e$ and countable, and if it's as an equivalence class of Cauchy sequences then it's uncountable, but you can't compare the two sets by looking at their elements because it isn't meaningful. Equality has to be taken in a broader sense here as not meaning exact set-theoretic equality, but rather equivalence. Different sets, same real number. $\endgroup$ – Matt Samuel Sep 15 at 23:06
  • $\begingroup$ @Doug: Your comments here seem almost dismissive of set theory, as something that you expected to be somehow "unique" but isn't. But again, go back to my answer, and actually read it. Are you surprised that there are different browsers (which in the past were almost incompatible with one another), or that there are different banks, different shops, or different operating systems? But if you want to buy a shoe online, which shop and which bank you use, and which delivery company does the actual delivery turn out to matter less to the end result of you having a shoe. $\endgroup$ – Asaf Karagila Sep 16 at 11:18
  • $\begingroup$ @AsafKaragila I've started a sandbox for a "canonical" form of this question here, as mentioned in the comments to the question. Feedback (from anyone!) is appreciated. $\endgroup$ – user1729 Sep 16 at 13:07
  • $\begingroup$ @AsafKaragila No, I'm not surprised by different browsers, different banks, or different shops. But also, there isn't a presentation of all those things as if they were one, unitary entity. The end result from purchasing things can differently significantly with respect to real world products. $\endgroup$ – Doug Spoonwood Sep 16 at 15:54
  • $\begingroup$ @Doug: Nobody presents constructions of the real numbers in set theory as "this is the only way to do it". $\endgroup$ – Asaf Karagila Sep 16 at 15:55
  • $\begingroup$ @AsafKaragila It does seem to me, and perhaps this is my mistaken impression, that set theory, or at least ZFC (yes, I know there exists other choices like Von Neumann's), gets presented as a single theory for mathematics. It doesn't seem so when talking about how just one real number might get constructed. $\endgroup$ – Doug Spoonwood Sep 16 at 15:59
  • $\begingroup$ @MattSamuel "Equality has to be taken in a broader sense here as not meaning exact set-theoretic equality, but rather equivalence. Different sets, same real number." I've been assuming that for all x, where x is a number, x = x. I don't see how equality fits here, because of the inequality of different construction of 'e's. I have to wonder if non-standard models might come into play here somewhere, given that x = x, gets suggested by one e having different members than another e. $\endgroup$ – Doug Spoonwood Sep 16 at 16:08
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Closed, Deleted

Please consider undeleting and reopening the post (question & answer both): Why integral of $dx$ is not $∫dxdx$.

This is a basic question came to OP's mind on the subject. There are a lot of people who have the same doubt about the fact. It will be very much helpful for those. Also my answer was accepted by OP and also being appreciated by the other members on this site. I think those question and answer are suitable for the site. I strongly recommend to undelete the post.

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Reopened

2 reopen votes left please:

Prove $ \lim_{z \rightarrow z_o} f(z) \in \mathbb{C}$ if $\lim_{z \rightarrow z_o} (z-z_0) f(z) = 0$

I made a new question, where I tried to be as clear and narrow as possible.

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Reopened


There have been at least five questions asking how to prove instances of the general proposition $\log_m(m + 1) > \log_n(n + 1)$ for integers $n > m > 1$:

1. How to know if $\log_78 > \log_89$ without using a calculator? (3 May 2012), with an exemplary answer by user22805.

2. Logarithm inequality problem: $\log_2 3 > \log_3 4$ (27 Sep 2016).

3. Compare $\log_34 $ and $\log_45.$ (24 Mar 2017).

4. How to compare logarithms $\log_4 5$ and $\log_5 6$? (25 Sep 2018).

5. Comparing $\log_5 6$ and $\log_6 7$ (9 Oct 2018).

There have been at least three other questions asking to prove inequalities of the form $\log_a{b} > \log_c{d}$ for integers $b > a > 1$ and $d > c > 1$:

6. Which is bigger among (i) $\log_2 3$ and $\log _3 5$ (ii) $\log_2 3$ and $\log _3 11$. (9 Jun 2013).

7. How can I compare $\log_2 3$ and $\log_3 5$ without using a calculator (5 Sep 2017).

8. Comparing $\log_2 3$ to $\log_3 5$ (6 Mar 2018).

There has also been at least one more complex question in the same broad category:

9.Prove $\log_{\frac{1}{4}} \frac{8}{7}> \log_{\frac{1}{5}} \frac{5}{4}$ (20 Sep 2012).

Most recently, the following question was posted, but it was quickly closed as a duplicate (I confess to being one of those who voted to close it):

10. Comparing logarithms with different bases (23 Oct 2018).

The close message for question 10 reads:

This question already has an answer here: How to compare logarithms $\log_4 5$ and $\log_5 6$? 6 answers

But the only method used to answer a previous question (1-9) that can also be applied to the present question (10) is to find positive integers $m, n$ such that $b^n > a^m$ and $d^n < c^m$ (as in Eudoxus's theory of proportion), so that $\log_ab > \tfrac{m}{n} > \log_cd$.

In a comment (which has now been incorporated into the text of the question), the questioner showed that he was aware of this method, and had already used it to answer his own question. He continues:

However, that method doesn't work for every example, and I wonder if there's a easier way to solve this?

Strictly speaking, any logarithm comparison question could be answered in this way. But that is not always very practical, because one one has to search for suitable values of $m$ and $n$, which may be quite large. Some previous answers state or imply the general rule that $\log_a{b} > \log_c{d}$ if $\tfrac{b}{a} > \tfrac{d}{c}$ and $a < b$, but that rule does not apply in this case. It is interesting to ask if some other rule might be applied, eliminating the need for a possibly haphazard search for $m, n$. Failing that, ad hoc solutions to the present problem are also of interest.

Question 10 meets MSE's selection criteria, so it ought to be reopened.

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    $\begingroup$ The question lacks contract in any event. Most importantly: why were the specific constamts in the problems chosen? If the problem is about arbitrary constants, it should be rewritten to say so. If the OP was already aware of a method to solve the problem, that context should also be in the post. Overall the post does.noy seem to demonstrate much effort to write a good post. $\endgroup$ – Carl Mummert Oct 28 '18 at 16:19
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    $\begingroup$ @Carl On that basis, Diophantus would have a hard time posting a question here! Where, in MSE's rules, does it say that every question must be framed in the most general terms possible? What is wrong with asking a question about particular numbers? Especially as no-one has (yet) posted a general answer or a general question covering this particular case. Finally, even if it were granted (purely for the sake of argument) that an experienced user ought to have asked a more elaborate question, shouldn't a new user be cut some slack? $\endgroup$ – Calum Gilhooley Oct 28 '18 at 16:28
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    $\begingroup$ @Carl Also, it was closed as duplicate, and my point is that it is not a duplicate. The close message is a false statement, and the close decision should be reversed. (Of course, anyone can also vote to close it for another reason, and no such person need feel obliged to vote for reopening.) $\endgroup$ – Calum Gilhooley Oct 28 '18 at 16:34
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    $\begingroup$ !Calum: there's no problem posting a question with specific numbers - but it is up to the OP to include adequate context, and the reason for choosing seemingly arbitrary numbers is (in my opinion) part of that context. If this was asked person to person at a department tea, we would expect the asker to say something about the numbers involved. The OP should be encouraged to improve the problem, they have plenty of "slack" to do so. $\endgroup$ – Carl Mummert Oct 28 '18 at 21:19
  • $\begingroup$ I think my guilty conscience over this has now been assuaged. :) $\endgroup$ – Calum Gilhooley Oct 29 '18 at 0:36
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Can this answer (on permutation groups) be undeleted:

https://math.stackexchange.com/a/3197094/10513

It was deleted for not providing an answer to the question. However, it gives a decent hint which leads to a solution. The hint is essentially "consider odd vs. even numbers". This was made formal in the accepted answer, which used mod 2.

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  • $\begingroup$ I think it's a bit of a stretch from that hint to the accepted answer. The hint ought to be a comment (in my opinion). $\endgroup$ – Gerry Myerson Apr 29 '19 at 12:50
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    $\begingroup$ @GerryMyerson Hints are a grey area. But I don't think deleting them because they are "a bit of a stretch" is the right thing to do. $\endgroup$ – user1729 Apr 29 '19 at 12:55
  • $\begingroup$ It would have been better, had a moderator converted the "answer" to a comment. You could try flagging the question for moderator attention, and making that suggestion. $\endgroup$ – Gerry Myerson Apr 29 '19 at 12:59
  • $\begingroup$ I flagged it beforehand, and was told to post my request here (admittedly i didn't suggest making it into a comment) $\endgroup$ – user1729 Apr 29 '19 at 13:19
  • $\begingroup$ OK, now you know what to do. $\endgroup$ – Gerry Myerson Apr 29 '19 at 13:22
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Undeleted, Merged and then deleted

Please reopen https://math.stackexchange.com/q/3208119/290189 since OP has self-deleted his/her own post after getting an answer. The community should have been given enough time to vote.

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    $\begingroup$ You can't reopen a question that isn't closed, GNU. Now it has been closed, as a duplicate, but I don't see how $x^y+y^x=(xy)^2-19$ is a duplicate of $x^y-y^x=xy^2-19$. So, I'm flagging for moderator attention. $\endgroup$ – Gerry Myerson Apr 30 '19 at 13:47
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    $\begingroup$ @GerryMyerson By the moment I posted this answer, I did voted to close this question as missing context. I did notice the difference between the two. Thanks for reminding me. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Apr 30 '19 at 13:52
  • $\begingroup$ @GerryMyerson a problem is that the original version of the question was incorrect. A third party edited it to this version, while main OP had re-asked a different version. $\endgroup$ – quid Apr 30 '19 at 15:32
  • $\begingroup$ I deleted it after the merge now. This did not work out ideally, but it's near impossible to fix. If somebody wants that version of the question on the site I recommend to ask it anew. $\endgroup$ – quid May 2 '19 at 18:17
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Deleted by a moderator

This question was closed and deleted with the reason given "This question is missing context or other detail". However the author of the question explained both his educational background (he is an undergraduate) and his motivation for the question (it was information that wasn't covered in his degree).

This information is sufficient context to give an answer, indeed I can't think of any further context that a person asking the question could add that would result in a better answer.

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    $\begingroup$ The body does not even contain the question. That question-post is poor, and the thread of very limited value overall. The answers being pretty terse and not giving enough detail. // Added: Given the comment below I'll add that it was not I that deleted it. $\endgroup$ – quid May 9 '19 at 6:59
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    $\begingroup$ As far as I can tell, if a post was deleted by a moderator - like in this case - the deletion cannot be reversed by regular users. (Of course, voting your posts still can show to which extent users support undeletion - and if there is some support, perhaps moderators might have a look at the the question again.) $\endgroup$ – Martin Sleziak May 9 '19 at 6:59
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    $\begingroup$ @quid can you explain what is poor about the question? Broadly speaking pen and paper methods of factoring numbers is a subject that the site should have coverage of. $\endgroup$ – Q the Platypus May 9 '19 at 23:32
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    $\begingroup$ I already mentioned one shortcoming. Further and more drastically, the question does not contain any relevant thought of the OP or even just explanation what they want that information for. For example, do they realize that one can easily recognize that some number are not prime? How would they approach the problem for two digit numbers? Or something else, would all make the question better. That said, the question would arguably be saveable. But what for? The answers are low quality. I'd prefer somebody, say my students, won't find any information here rather than those answers. $\endgroup$ – quid May 10 '19 at 9:55
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    $\begingroup$ Fortunately similar information is available in other and better threads. In my opinion, the site is quite simply better without this thread. $\endgroup$ – quid May 10 '19 at 9:57
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Please unmark the duplicate of this question. I have clearly said that my question has nothing to do with duplicate one. I am asking totally different thing and the duplicate question's answer does not help me at all. It is also an unique question which follows m previous question.

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    $\begingroup$ I don't believe the relationship between the Questions is quite so simple as one "has nothing to do with" the other. Both involve intersections between two spherical caps, although you might not have visualized your problem in this way. There might still be a further problem in stating the area in terms of how you parameterized the spherical region, I grant, but it would be worth understanding the solution of the proposed duplicate to try restating the area given there in your terms. $\endgroup$ – hardmath Jun 6 '19 at 17:11
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Undeleted, reopened

Please consider undeleting this old post: Show that a function $f:P(X)\to P(X)$ preserving the subset relation has a fixed point

It was created on Sep 17 '16, has two good answers.

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    $\begingroup$ It seems to be a special case of this question, and Aloizio's anwer in fact answers the general question. So if the goal is to preserve answers, the logical thing to do would be to move them there. $\endgroup$ – Arnaud D. Jun 28 '19 at 13:48
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    $\begingroup$ It seems to me the Question at issue here has the more general formulation (it does not require an "increasing" function). In any case I've voted to reopen as the Question at issue meets my threshold for context (and it otherwise also on-topic). $\endgroup$ – hardmath Jun 30 '19 at 19:45
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    $\begingroup$ I disagree with your assertion that the question has two good answers. It has one good answer, and a hint. The question itself is not good at all. I am content to see the question left undeleted, but I see no reason to reopen it. Arnaud D.'s suggestion is, I think, preferable. $\endgroup$ – Xander Henderson Jun 30 '19 at 23:51
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    $\begingroup$ "I am content to see the question left undeleted." Well, that is what my proposal is. I agree that the question itself was not good enough and thus I did not ask for reopening. @Martin Sleziak has added useful information to the post. (Thanks!) Also, Aloizio's good answer mentions at the beginning "the nice answer by @Brian". $\endgroup$ – Jack Jul 1 '19 at 1:47
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Undeleted, deleted, undeleted, reopened

Please consider undeleting this post: What is the formula of this angle?

There is a well written and well-received answer to this interesting question.

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Undeleted, deleted, undeleted

Please undelete and consider reopening this post: Show this equation has every positive integer as solutions

OP did give his thoughts. NOT a no-context question. And there are two good answers.

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Undeleted, deleted, undeleted

Please consider undeleting this post: How to evaluate $\lim_{x \to 3} (x^2-5x+4)^{x-3}$, which is clearly not a zero-effort question.

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    $\begingroup$ You say that the question should be opened because it is "clearly not a zero-effort question." This seems to imply that the question was closed because it "lacks effort". However, "lacks effort" is not one of the close reasons used on MSE. Indeed, I see that question was closed for "lacking context". For example, a description of what theory the asker is familiar with and what course they are taking. Are they expecting a computation involving $\varepsilon$s and $\delta$s? L'Hospital's rule? What? The question should be deleted. $\endgroup$ – Xander Henderson Aug 15 '19 at 12:31
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    $\begingroup$ Moreover, examining the comments attached to that question, it is not even clear where the function being discussed is meant to be defined. Is it a real function with a very "hole-y" domain? or a complex function, in which case one needs to consider branches of the logarithm? It is not a good question. $\endgroup$ – Xander Henderson Aug 15 '19 at 12:34
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Deleted, undeleted, deleted, undeleted, deleted, undeleted, reopened, closed as duplicate, deleted, undeleted

What OP wrote under the problem statement clearly show his/her thoughts:

How can I do this if I don't know how $a_n$ is defined? I can use the given limit to get the range of $a_n$ in terms of $L$, but I lack the direction to complete the proof.

This is not a zero effort question. Please consider undeleting this post:

Given positive sequence $a_n$ where $\lim _{n\to \infty} a_n = L, L >0$, prove that $\lim_{n \to \infty} 1/a_n = 1/L$

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    $\begingroup$ Did you check if it's a duplicate? It's a very standard question. $\endgroup$ – quid Apr 26 '19 at 14:32
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    $\begingroup$ @GerryMyerson a question might be eligible for closure for multiple reasons. It's maybe not a PSQ in it's purest form, but it's still not a good question. I'd say if somebody wants to restore a question it's on them to make sure no reason applies not just the one that was chosen. Further, it would have been on the asker to make some good faith effort to find a dupe before answering (and then complaining that their answer was removed). If a dupe of this question is not findable what does this tell about the level of organization in those tags. The priorities are not good. $\endgroup$ – quid Apr 27 '19 at 7:12
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    $\begingroup$ @GerryMyerson here math.stackexchange.com/questions/1171733/… it was pretty trivial to find. $\endgroup$ – quid Apr 27 '19 at 7:22
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    $\begingroup$ Well, in any case they complain. We can replace the "that" by "after". On the rest, again the onus is on them. They ought to explain that there is no dupe (supposedly). Further, it is generally considered as good form to mention if one has answered oneself. Especially if it is the only answer. @GerryMyerson $\endgroup$ – quid Apr 27 '19 at 7:26
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    $\begingroup$ @GerryMyerson not sure about that. I might have had the luck to use the better strategy for that example, searching for words via Google on this site not for formulas for example 'convergence of inverse of convergent sequence' works well. $\endgroup$ – quid Apr 27 '19 at 7:31
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    $\begingroup$ @GerryMyerson (and quid) I did try to find a duplicate and I indeed noticed that limit of reciprocal of a sequence away from zero should be a rather standard exercise in calculus/analysis and should have been asked before. However, I think "context" counts as an integral part of a post, and that is why we insist on "contexts", don't we? [cont.] $\endgroup$ – Jack Apr 27 '19 at 13:14
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    $\begingroup$ [cont.] I am not able to find any same/similar confusion ("How can I do this if I don't know how $a_n$ is defined?") in any known post, for instance in the linked post in one of quid's previous comments and thus I do not think this post should be considered as an "absolute" duplicate that one should delete it. $\endgroup$ – Jack Apr 27 '19 at 13:14
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    $\begingroup$ I agree with Jack's comments above, I don't think this post should be closed if a duplicate is not found where the same confusion is addressed. To the best of my knowledge, this confusion has not been addressed before, so this post should be undeleted and reopened. $\endgroup$ – user279515 Apr 28 '19 at 5:43
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    $\begingroup$ @GerryMyerson Basically a duplicate, except it doesn't require $a_n$ to be a positive sequence, was asked fairly recently at Sequence Limit Reciprocal Law Proof, where I provided an accepted answer. As for finding it, note it originally only used the tag "elementary-number-theory", but I changed it later to "limits", so searching for it initially might not have turned it up. However, I can't see the original deleted question content, but the page it brings up shows $2$ other somewhat related ... $\endgroup$ – John Omielan May 2 '19 at 8:08
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    $\begingroup$ (cont) questions: Given: $\lim\limits_{n\to\infty}a_n=0$ prove $\lim\limits_{n\to\infty}\frac{1}{a_n}=\infty$ and How to formally prove that if $\lim \limits_{n \to \infty}a_n=\infty$, then $\lim \limits_{n \to \infty}\frac{1}{a_n}=0$.. Although they're somewhat different, and I haven't checked them carefully, I suspect their techniques are transferable. $\endgroup$ – John Omielan May 2 '19 at 8:09
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    $\begingroup$ The status of the question had not changed at all. What is the justification for this edit? $\endgroup$ – quid May 31 '19 at 16:57
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    $\begingroup$ On the comments above, which I only see know, due to lack of a notification, that's not a particular confusion. Any generic proof will necessarily do just fine to address this. I mean the proof you gave is completely generic. What do you think you did to address whatever specific confusion? $\endgroup$ – quid May 31 '19 at 17:04
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    $\begingroup$ I agree with Brahadeesh's comment and I've undeleted the question. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Jun 14 '19 at 9:21
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    $\begingroup$ @quid The quoted question in Jack's last comment answers your first question; point (3) in Jack's answer addresses your second one. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Jun 16 '19 at 3:17
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    $\begingroup$ @GNU As detailed this ask nothing more than that the author understands that they might be able to do it or at least how to strat for a specific sequence like say $2n/(n+1)$. Any generic proof will do just fine, and what about the third point? Again any proof will have to address this somehow (in one based on continuity it might be hidden). Certainly it's findable in other answers. It's just a contrived argument to save this post, and frankly I am appalled by this. Explain how this answer math.stackexchange.com/a/1171755 is not sufficient or math.stackexchange.com/q/54754? $\endgroup$ – quid Jun 16 '19 at 8:51
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Undeleted, deleted, undeleted, deleted, undeleted

I nominate Optimization problem for routes for undeletion because the question asker self-deleted his question shortly after receiving an answer.

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Deleted, undeleted, deleted, undeleted, reopened, closed as duplicate

Please reopen Calculating the summation$\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}$ because it's not an elementary question and OP has tried checking the proposition using Wolfram Alpha.

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    $\begingroup$ In my opinion it's very poor style to reignite this after month without mentioning any of the earlier activity in which you even were involved. Thus, I locked the post for now. $\endgroup$ – quid Apr 30 '19 at 11:43
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    $\begingroup$ I'm puzzled. A "content dispute" notice was lifted in March 2018. The content has not been altered since then. So it seems strange to lock it for "content dispute" now, @quid. [I guess I should mention that I was involved in earlier activity.] $\endgroup$ – Gerry Myerson Apr 30 '19 at 13:56
  • $\begingroup$ @GerryMyerson Are your really puzzled or are you just searching an argument? First, the content of the post was also not changed between the first locking and the first unlocking. Second, the lock was not lifted in the sense of somebody lifting it, it simply expired. It was not reinstated as there seemed no need back then about a year ago. Then half a year ago, there was one more round of undelete-delete but it fizzled out quickly. Now somebody wants to go back to this again, indeed without any further changes, simply picking up the del-undel again. To prevent this, I locked it. $\endgroup$ – quid Apr 30 '19 at 14:36
  • $\begingroup$ Third, it might be relevant to note that the lock was "lifted" while the post was deleted. Thus, if consistency is the concern of course I should lock it again now. I could also have it become undeleted and then personally delete it again. Last time around some where keen on locks being used. So, there you go. Of course that's not fine for you now either, presumably because it does not cater to your personal preferences. $\endgroup$ – quid Apr 30 '19 at 14:43
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    $\begingroup$ To sum up, I locked it to prevent the delete-undelete cycle being restarted. By now the question was deleted four times. Plus it is an odd situation, in that it first got siginificantly improved by a third party only for this then being undone If anything should happen likely a completely new version should be posted. This would be a reasonable thing to do if preserving content is the actual goal. Of course if playing un-del games should be the goal... thus locked. @GerryMyerson $\endgroup$ – quid Apr 30 '19 at 14:48
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    $\begingroup$ @quid, when I write that I am puzzled, please do me the courtesy of accepting that I really am puzzled. I'm puzzled not so much by the locking but by the phrase, "Content dispute", when there was no change in content. Had the locking notice said "Prevent delete/undelete cycle" I don't know that I would have made any comment. Does a moderator have the option of inserting custom-made locking notices, or is "Content dispute" the only phrase available? Also, I always assumed that when a moderator locked a question, the question stayed locked until a moderator decided it was time to unlock it.... $\endgroup$ – Gerry Myerson Apr 30 '19 at 22:46
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    $\begingroup$ ....I didn't know that locks expired of their own accord after a week. I've been here almost a decade, and I'm still learning how the place works. $\endgroup$ – Gerry Myerson Apr 30 '19 at 22:47
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    $\begingroup$ @GerryMyerson the list of reasons is fixed (we can ask for additions in principle but not spontaneously) "content dispute" is the one commonly used in this case, others are "off topic comments", "contest question", "cw answer", "historical significance". We can lock for an hour, for a day, for a week, or permanently. Usually one tries to avoid permanent locks. $\endgroup$ – quid Apr 30 '19 at 23:58
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    $\begingroup$ Probably it's worth mentioning that there already is one answer in this thread about the same question. $\endgroup$ – Martin Sleziak May 15 '19 at 7:34
  • $\begingroup$ @quid, thanks for the explanation about length of locks. It's not possible, is it, for non-moderators to see what length a moderator has chosen when that moderator locks a question? $\endgroup$ – Gerry Myerson May 20 '19 at 4:26
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    $\begingroup$ @GerryMyerson indeed I think that's not possible. $\endgroup$ – quid May 20 '19 at 8:39
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Undeleted, reopened

Please undelete and reopen this post: Evaluate this limit: $\lim_{n \rightarrow \infty} \frac{n\sin n}{2n^2 - 1}$

This post is by no means missing context. OP clearly stated at the beginning what he/she tried and where he/she got stuck. This post has also a detailed answer by a 50K+ user.

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    $\begingroup$ It might be worth noting that unfortunately that so-called detailed answer completely ignores the provided context, in that sense it's a rather poor answer, but arguably that's tangential. I'd tend to agree that this question does show reasonable context. If we take the context into account, likely it's a dupe. $\endgroup$ – quid Sep 23 '19 at 15:52
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    $\begingroup$ Instead of saying "what goes wrong with my thoughts" or "how can I go on with my original approach", OP explicitly stated that "Any help will be appreciated". And @Clement C. helped this user by directly giving an argument. Not a poor answer, and there have four people considering it good. This post is an extremely poor choice for deletion. $\endgroup$ – Jack Sep 23 '19 at 15:58
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    $\begingroup$ quid does make a fair point that an answer showing how OP could go on with the original approach may be more useful for the asker. One could add such an answer after this post is reopened. $\endgroup$ – Jack Sep 23 '19 at 16:06
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Undeleted, reopened

Please undelete and reopen this post:

How can one use the direct comparison test for $S=\sum_{k=1}^{\infty}{\frac{1}{\sqrt{k}+10k}}$?

Even in the very first version of the post, OP states his/her thoughts and difficulties he/she has. This post is NOT missing context. And it is NOT a duplicate of any other question.

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    $\begingroup$ Because we already have many questions where divergence of a series is deduced from a comparison with the harmonic series, this is bound to be a duplicate dozens of times over. Therefore the question should also be closed as too localized (not adding anything new to the site, and only helping the asker do their homework). Missing context is the best proxy we currently have, so if reopened I will vote to reclose and redelete. $\endgroup$ – Jyrki Lahtonen Sep 30 '19 at 4:53
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    $\begingroup$ @JyrkiLahtonen Maybe I should have trie to search a bit more, but by a quick search I only found this: Calculus II: Comparison Test for Divergence $\sum\limits_{n=1}^{\infty}\frac{1}{n+\sqrt{n}}$. (All I am saying that I am unable to confirm that there are dozens of posts which are close to duplicates. Although I agree that when I saw the question, I expected that there should be many similar questions.) $\endgroup$ – Martin Sleziak Sep 30 '19 at 8:09
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    $\begingroup$ @MartinSleziak It is one of the standard series to use a comparison test with :-) Anyway, when the question is a (near-) duplicate IMO showing effort/thoughts is NOT SUFFICIENT to stop closure/deletion. The questions should have wider interest, and the context should demonstrate that. $\endgroup$ – Jyrki Lahtonen Sep 30 '19 at 9:59
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    $\begingroup$ Mathematics Stack Exchange is a question and answer site for people studying math at ANY level and professionals in related fields. How many questions a student asks are not supposed to be "standard"?! And is any one of the four mentioned in the first comment not standard? $\endgroup$ – Jack Sep 30 '19 at 11:59
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    $\begingroup$ @Jack Your comment about MSE being for questions at any level is a red herring---the question was not closed because of its level. The question is a standard question which occurs (in one form or another) in many elementary texts on calculus. Moreover, it is a question which already has an answer on MSE. What new, valuable information does this particular question add to MSE which isn't already on the site? $\endgroup$ – Xander Henderson Sep 30 '19 at 20:18
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    $\begingroup$ How many questions a student asks are not supposed to be "standard"?! @Jack, not very many. The same applies to StackOverflow. Which is exactly why Jeff Atwood wrote that a new asker should spend 98% of their time on StackExchange searching. Getting more and more questions does not improve the site, and is not necessary for its success any longer. On occasion it is quite the opposite. $\endgroup$ – Jyrki Lahtonen Oct 1 '19 at 14:06
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Undeleted, deleted, undeleted, reopened, closed as duplicate, deleted, undeleted, deleted, undeleted

Please consider to undelete this question.

The OP brings some background about the problem and is just trying to find an easy solution. The one provided by me looks quite unknown (as it seems from the comments and the answers) thus I think it can be of future help if the question is undeleted.

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    $\begingroup$ It's good form to disclose that one has an answer on the post oneself. $\endgroup$ – quid Aug 15 '19 at 21:00
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    $\begingroup$ This question is a duplicate of many other questions on MSE. While I don't think that it is worth keeping (it brings nothing new to the table), if it is going to be kept, it should be closed as a duplicate. I left comments indicating a couple of potential dupe targets. $\endgroup$ – Xander Henderson Aug 17 '19 at 15:05
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    $\begingroup$ On the contrary I believe it brings something new to the table. My solution is different than any other from all the linked posts. $\endgroup$ – Zacky Aug 19 '19 at 20:24
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    $\begingroup$ @Zacky In that case your answer will stand its ground as an answer to the duplicate target as well, and you might consider relocating it there! Just by posting a new answer, the thread of your choice will be bumped to the front page, meaning that many viewers will see it and be able to vote it. <- This could be my template reply to all the users who are sad about a deletion of a duplicate. They can easily save their work this way! $\endgroup$ – Jyrki Lahtonen Aug 30 '19 at 18:19
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    $\begingroup$ "Partial fraction without defraction for an integral" What the heck does that mean? Is defraction really a word? Why has no one edited that title to something intelligible? $\endgroup$ – Gerry Myerson Aug 30 '19 at 23:00
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    $\begingroup$ @GerryMyerson I think that no one had edited the title into something intelligible because no one actually knows what the asker intended. That is part of the problem with the question (aside from the fact that it is a duplicate). $\endgroup$ – Xander Henderson Aug 31 '19 at 14:17
  • $\begingroup$ @Zacky Honestly, I think that Jyrki's advice is good advice. Indeed, I think that your answer would be a better fit for one of the other questions, if for no other reason than the current question specifically asks about partial fraction decomposition, while the others don't. Your answer would be a better fit for a different question. $\endgroup$ – Xander Henderson Aug 31 '19 at 14:18
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    $\begingroup$ @XanderHenderson something looks off. You said that it brings nothing new to the table and it's not worth to be kept, you even ranted on how my answer isn't a "pedagogical". Are you sure that you honestly believe that is a good advice? $\endgroup$ – Zacky Sep 1 '19 at 8:52
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    $\begingroup$ I also wrote in my pre-edit for OP: "Since this is just for your training, here's a more different approach for it. If it doesn't fit for you, I will delete it (it doesn't use any partial fractions)", when OP commented I think I received a positive feedback about it from OP.// Indeed it doesn't answer the exact question, but another answer (which got accepted by OP) shows a way with partial fractions. I only posted my answer after I saw it, and after the comments (from some high-rep users) who encouraged OP to not look for a better way? $\endgroup$ – Zacky Sep 1 '19 at 8:58
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Reopened, undeleted, closed, reopened

Please consider undeleting this question where I also provided an answer: Integrating $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx$ with restricted techniques.

The OP from clearly provides background on how the integral appeared, although it was some kind of homework now it can be useful for others too.

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    $\begingroup$ It's good form to disclose that one has an answer on the post oneself. $\endgroup$ – quid Aug 15 '19 at 20:59
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    $\begingroup$ Hope I don't sound rude, but I don't understand what you wrote even with translate. Did you meant: It's a good thing to mention that I posted an answer to the linked question? $\endgroup$ – Zacky Aug 15 '19 at 21:07
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    $\begingroup$ Yes. You should mention this. It makes clear that you are not a neutral third party. You have a personal interest in the undeletion. This does not disqualify you from making the proposal. But it is good form to be upfront about it. $\endgroup$ – quid Aug 15 '19 at 21:12
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Undeleted, Deleted, Reopened, Undeleted

Please undelete and reopen $\sum_{i=1}^n\frac{x_i}{\sqrt[nr]{x_i^{nr}+(n^{nr}-1)\prod \limits_{j=1}^nx^r_j}} \ge 1$, for all $x_i>0$ and $r \geq \frac{1}{n}.$.

  • This inequality question is clearly a conjecture made from an existing question, which I think is a fair question to ask. Inequality conjectures on this site are often false. This is one of the rare cases where experiments yield correct claims. I expect that there are many inequalities that can be inferred from the inequality in question (such as this one, this one, this one, Comment 5 of this one, and even Comment 1 of this one). We should preserve it, to keep it a reference.

  • The current answer (mine) is unsatisfactory, for it is long and too complicated. This is not an easy inequality problem, and there should be a better way to solve it. If my having posted an answer there is an issue for some users (which I don't understand why, it is not like reputations grant anything to me), I can make my answer a community wiki post. Knowledge, on the other hand, is precious (and reputations are not at all precious, which is perplexing to me because a lot of arguments here are based on reputations, e.g., reputation farming, who benefits from undeleting some posts, etc).

  • This is not a contextless question. Users are often asked to provide a context, and the source of the problem is a context. The asker stated that this was modified from an old question. You might think this is insufficient. I disagree, but anyway, more context has been added.

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    $\begingroup$ You should note that the question, which is a contextless problem statement question, currently has only one answer, which was written by you. You are not a disinterested third party in this case. $\endgroup$ – Xander Henderson Jul 2 at 5:06
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Undeleted, Reopened

Please undelete and reopen Proof of $(1 + \delta)^{1/2 + \delta}(1- \delta)^{1/2 - \delta} > 1$ for $0 < \delta \leq 1/2$?. Let it be known that I answered the question. The question should now have sufficient context.

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Reopened

Please consider this question Prove that $\gcd\left(n^{a}+1, n^{b}+1\right)$ divides $n^{\gcd(a, b)}+1$ to be reopened. I answered the question. And more context has been given.

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    $\begingroup$ You should, perhaps, note that you answered this question, and received a bounty for that answer. Hence you are not a disinterested third party. $\endgroup$ – Xander Henderson Jul 19 at 14:25
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    $\begingroup$ What's the point of undeleting the post after it is reopened? You have nothing to request. $\endgroup$ – Arctic Char Jul 19 at 15:33
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    $\begingroup$ @ArcticChar I didn't undelete it. $\endgroup$ – Shubhrajit Bhattacharya Jul 19 at 15:34
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    $\begingroup$ @ArcticChar I actually rather disagree. A record of the activity should be kept at least for some time. $\endgroup$ – quid Jul 19 at 16:31
  • $\begingroup$ I guess Shubhrajit just deleted another request, @quid (I don't have 10k to see what exacfly happened) $\endgroup$ – Arctic Char Jul 24 at 4:18
  • $\begingroup$ @ArcticChar I have deleted my request. Always my requests get downvotes. I answered and invested time for them. Why can't I just request for questions to be reopened which are answered by me? I don't want to make any further requests. I started to hate MSE for many reasons including bad and unfriendly behaviour from users. $\endgroup$ – Shubhrajit Bhattacharya Jul 24 at 5:47
  • $\begingroup$ @ShubhrajitBhattacharya You do get positive net votes for quite a number of your request, and quite a lot of your request resulted in reopening/undeleting, so I don't see why you seem to be upset.... $\endgroup$ – Arctic Char Jul 25 at 7:14
  • $\begingroup$ @ShubhrajitBhattacharya While it is fine to request reopening/undeleting of posts that you are involved, we suggest users to explain why actions should be taken. The reason "I have answered the questions/ I have spent time on it" is not a very strong reason. $\endgroup$ – Arctic Char Jul 25 at 7:17
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Reopened

I propose to reopen Which Combinations of Roots of Unity are Zero?, which is a perfectly phrased and interesting question of which I have no idea why it had been closed. There was some debate about whether the questioner meant to ask for real or integer linear combinations of the roots of unity, which is now settled by an edit – it’s about integer combinations. (But even the version with real coefficients would be interesting and worthy of this site, in my opinion.)

It would also be nice to hear from the ones who have closed the question or are in favour of leaving it closed as to why this question should be closed. I have not the slightest idea.

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$\begingroup$

Undeleted, Reopened

I would like to request that this thread be undeleted and reopened: "If $\#(S)<\#(\Bbb N)$, then prove that $S$ is finite, without using the Axiom of Choice.." I did not answer the question, but I think the thread is useful for people to learn which argument relies on the Axiom of Choice, and which does not.

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  • 1
    $\begingroup$ I am confused why my undelete vote wasn't there. Maybe I forgot to vote myself. What a blunder! I might have forgotten to vote to reopen too. However, I might also have voted to reopen, but the reopen vote might have also expired. $\endgroup$ – Batominovski Jul 29 at 11:53
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