# Requests for Reopen & Undeletion Votes (volume 07/2018 - today)

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).

Some guidelines:

• Please be polite, and respect the many different viewpoints in our diverse community. This goes for the person making the request as well as those commenting on it.

• There is a reopen queue. Please wait until a post has gone through this queue, before posting here. Notice that the first edit after the question was put on-hold pushes the question into reopen review queue, if the edit was done within 5 days of closure. So does a reopen vote. (If the review has already been finished, it is shown on the timeline of the question.) In doubt, wait 24 hours after the last substantive action.

• To inform readers of the current (and past) states of the targeted post, please add once the request resulted in some action the information Reopened or Undeleted at the start. (If it the action is undone, add this too, like Reopened, reclosed.)

• Do not only post a request, like "request reopening of ". Instead make a case for your concern. Yet keep in mind that it can be easier to get your request handled if you try to frame in a away that takes the feedback the post received into account in a positive way rather then seeking confrontation. Also, try to improve the post before posting here.

• In case of "small" requests, like one missing vote, it can make sense to ask in chat instead of posting here. The room CRUDE is a reasonable place for such requests. The same guidelines apply there.

Earlier versions of this thread that served as a model:

Undeleted

Please undelete A probability to 6 in a dice since OP has self-deleted his/her own question after receiving an answer. This isn't fair to the answerer because his answer deserves review from the community.

Please undelete A contradiction in calculating the legendre symbol and https://math.stackexchange.com/q/3224172/290189 because OP's have self-deleted their question after receiving an answer from others.

• I undelete both. At least for the one, it'd also have been possible to let it deleted as it was a relatively simply oversight. It's not clear there is any value in keeping that around. But there is also no harm, so. – quid May 14 '19 at 15:31
• Please adhere to the "one request per answer" format; having multiple requests in the same answer makes it difficult to track changes. – Brahadeesh May 15 '19 at 8:03
• @Brahadeesh Thanks for your comments. I'll beware of this practice next time. – GNUSupporter 8964民主女神 地下教會 May 15 '19 at 9:00

Undeleted.

Please undelete Bounding the number of edges in a graph satisfying a certain property since the question asker has self-deleted his/her question after receiving an answer.

Closed, deleted, undeleted, deleted, undeleted, deleted, undeleted, deleted, undeleted, reopened.

Unfortunately, the question I asked Why is the zero polynomial the only one to have infinite roots? was put on hold as off-topic first, then closed, and then deleted. I edited it much for it to be reopened, but it wasn't reopened. I apologise if it was off- topic to you, but I edited it. If it being off topic yet, kindly suggest improvement or undelete it please.

Note (quid): I reopened this now. The mass-editing and double posting OP is gone, the question is simple and a bit confused, but arguably not overly contrived and understandable, and answered. It's not impossible somebody else might find this useful at some point. Let's move on.

• Have you finally made up your mind between "Wikipedia" and "wikipedia"? – Did Feb 3 '19 at 21:37

Undeleted

Intersection of Normal closure and Center

The OP deleted question after answer was given.

• I undeleted, but maybe write a proper answer next time. – quid Jun 4 '19 at 13:39
• @quid I like hints (plus its a pretty straightforward question - I spent a while debating whether to just leave it at "kill $t$"). – user1729 Jun 4 '19 at 13:43
• Then maybe start a Q&H site. This is Q&A site. – quid Jun 4 '19 at 18:09
• @quid the hint was clearly sufficient for the OP - they wouldn't have deleted their question otherwise! :-) – user1729 Jun 4 '19 at 19:00
• That's pretty irrelevant to my point. Further, If "sufficient for the OP" is your main concern, why do you bother us with an undelete request? // The way that hint was orginally presented to me personally made it pretty confusing. The new format is in a way better. But, frankly I just despise that form. I know it's popular but I think it's terrible style. – quid Jun 4 '19 at 22:55

Reopened, closed

Please consider reopening (also for the sake of avoiding further unreasonable strong action of deletion, there has been a delete vote already): How to show for $$x\in \mathbb{R}$$, $$|x|\leqslant 1+x^2$$

This is completely a legitimate question to ask for a beginner. Also, OP did show his/her work in the post, although he/she did not notice what he/she proved is actually a stronger result. Furthermore, it has very well written answers.

I feel it very harsh to close/delete such posts.

• I'd agree with Jack's assessment that the OP already has $2|x|\le1+x^2$ and they missed that this implies the result - and this should count towards context. It would be nice if the OP included how they got $2|x|\le1+x^2$, even if only as a link to some place where this is proved - but since the OP hasn't been seen for a long time, it is unlikely that they add this to the post now. – Martin Sleziak Aug 29 '19 at 7:14
• I'm a bit hesitant to call this "legitimate question to ask for a beginner". It seems to me that noticing that $|x|\leq 2|x|$ and knowing that order is (by definition) transitive is more basic than proving $2|x|\leq 1+x^2$, so I would interpret the question more as the OP having been just momentarily distracted. I doubt it's really necessary to keep that question and its answers. – Arnaud D. Aug 29 '19 at 10:39

Undeleted, deleted, undeleted, reopened, put on hold, deleted, undeleted again (the war goes on)

The topic starter solved this problem by using "differentiation or Lagrange multipliers", but he looked for a short solution and he got it.

Thank you!

Undeleted, Reopened

Please consider undeleting and reopening this post: Convergence or diverge of the series $$\sum_{n=1}^\infty\left(\frac{1}{n} - e^{-n^2}\right)$$

OP clearly indicated his/her thoughts at the beginning of the post, and there is a well written (with 10 upvotes) answer.

Undeleted, reopened, closed

What is the maximal number of subsets of a finite set, such that no one is the unions of some other ones? is a serious mathematical question which has attracted two useful answers (full disclosure – one of those two answers is mine). Please have a look and consider casting the third vote to undelete.

Undeleted, deleted, undeleted, deleted (mod)

Please consider casting the final undelete vote to this post:

Which among the given series converges

This is not a zero effort post: OP has ruled out some choices for the problem and has reduced the problem to a simpler one. This is a good attempt. Also, @Theo Bendit has posted a well written answer.

Mod comment (quid): I deleted it as the question remains unclear in its formulation. As such it has the potential to create confusion and in any case the mathematics is well-known and in one way or the other certainly on the site. It is good that OP apparently got competent help. This does not alter the fact hat preserving the thread as is in my opinion does not ad value to the site and to the contrary degrades it (adding a confusing question). If somebody want to preserve the answer they should have improved the question, or create a separate one. That's still an option.

• The asker has not ruled out several choices for the problem. The problem is not a multiple choice question. Rather, they were asked to examine each of those four series, and determine which converge. If anything, the question is four distinct true / false questions (making it "Too Broad"). – Xander Henderson Jul 28 '19 at 16:18
• Moreover, you claim that it is not a zero effort question. Even if I agreed with you regarding the idea that "showing effort" is, in and of itself, sufficient context, I disagree about the effort which has been shown. The question is ultimately about one of the four series being presented, and there is no work shown for that series. For the remaining three, the asker claims to have already found appropriate counter-examples, but don't actually show any of that effort. Claiming to have done something is not the same as demonstrating it. – Xander Henderson Jul 28 '19 at 16:18
• "The problem is not a multiple choice question. ... which converge." One could turn almost all the multiple choice problems into non-multiple-choice ones in such a way. The rest of your comments are based on this biased assumption. "the asker claims to have already found appropriate counter-examples, but don't actually show any of that effort." OP summarized as partial work that three items haven been done and now he/she focuses on item (c). Not guilty. The strong action of deletion of this post is unreasoning. – Jack Jul 28 '19 at 17:30
• The question consists of four different T/F questions. It is not a single multiple choice question. There are four different questions here. Determining the truth or falsity of parts (a), (b), and (d) does absolutely nothing to shed light on (c), especially considering that the asker doesn't actually show any of their work, but simply states that they have already completed those parts. It lacks context and is too broad. It was rightfully closed and deleted. – Xander Henderson Jul 28 '19 at 18:16
• One has to wonder how they could show b yet not c. Makes one wonder of the merits of their undisclosed approaches. The paraphrase in meta OP is false as pointed out by @XanderHenderson and your reply is strange in that the critique of you paraphrase (not even the main OP) was not that the question is a multiple choice question but rather that there is not partial progress to the question asked. The best one can say is that the question is not 'several questions asked in one' (contrary to what one might think) and the Q provides some limited context by giving related problems they can solve. – quid Jul 30 '19 at 11:47
• I'd say if they had sketched their solutions to those they can solve, it might be sufficient context. As is, it does not add all that much, especially since the partial progress is implausible. Indeed it appears it is partly false as they might have misunderstood the question (the meaning of necessarily). Of course, it's anyone's guess since they do not provide the claimed solutions. Clear case of actual lack of context; we cannot identify the extent of the problems of OP. – quid Jul 30 '19 at 11:50

Undeleted, deleted, undeleted, deleted, undeleted, deleted, undeleted, delete (mod)

Please undelete this post Map subset of a group to zero?

This is not a trivial exercise. It has a very detailed thoughtful answer by @Arturo Magidin.

Mod comment (quid): I deleted this one, as the question-post is still not clarified and the thread including the answer post is a back and forth. Like: "It cannot be this, you may mean that. Oh, now you said it's about something else." I am glad that OP was helped, but I think there is no archival value to this in its current form. As usual, those that want to can extract whatever they think is valuable, via edits or moving of content.

• If you plan to keep saying things like "Redeleted (6/17/19) by a same group of users. One initiated three times the delete votes and one voted three times to delete this post. – Jack Jun 17 at 22:01" you might refrain from voting to undelete repeatedly, especially on posts where there was not recast delete vote prior to that. (There is now though.) – quid Jul 13 '19 at 15:43
• There has been no action whatsoever (to my knowledge) from mods or the system to prevent casting/initiating deletion votes for some particular posts over and over again by mostly same group of users. It is not difficult to count such instances. I assume from such observation that repeated voting is not discouraged in general. "If you plan to keep saying things like" This is an absurd and highly misleading comment from a moderator: your quoted comment refers to one particular proposal and I have never said it somewhere else. – Jack Jul 13 '19 at 18:09
• I take it you do not plan to keep saying things like the one I quoted, then. Well you did say "On the other hand, what one can see from the timeline is that a user voted to delete the posts twice while there are people who hold different opinions have already voted to undelete and reopen the post." which also raises double-voting in a critical way. – quid Jul 13 '19 at 18:57
• There has been no action whatsoever from mods or the system to prevent casting/initiating undeletion votes for some particular posts over and over again by mostly same group of users either. – Jyrki Lahtonen Jul 14 '19 at 16:26
• @quid I think a mod deletion was highly improper here. Sad to see you once again forcing your personal opinions onto the community. These decisions should be made by the community - not an individual. – Gone Aug 4 '19 at 15:24
• @Bill after about ten changes of status I think it's about time somebody decides it one way or the other. Visibly the community did not reach a solution. – quid Aug 4 '19 at 15:26
• @quid "Changes of status" are not harming anything. There have been more in the past and they eventually settled down. – Gone Aug 4 '19 at 15:27
• @Bill it's a distractions, possibly confusing, and bumps this meta post. Certainly there are worse things, but I consider it as fundamentally unreasonable to have "blinking" posts that are un-deleted every other day or every other week. (This one is going on since a month.) – quid Aug 4 '19 at 15:29
• @quid I think there are for more important matters that deserve to be deemed "fundamentally unreasonable". This shouldn't even be on the radar. – Gone Aug 4 '19 at 15:32
• @BillDubuque examples? – quid Aug 4 '19 at 15:33
• @quid One of the reasons that I initially created this thread (original version) was so that there would be only one thread being bumped on such matters. The bumps are expected and are completely normal. Those with no interest in such matters can easily ignore it. – Gone Aug 4 '19 at 15:42
• @BillDubuque that's fine it does however not address the other points and does not provide any examples. Anyway, if you see things that I or another moderator should address please bring them to our attention. If you want to discuss this particular post in more detail, post a question about it. – quid Aug 4 '19 at 15:49

Undeleted, deleted, undeleted, locked and merged with duplicate (mod)

Please consider undeleting: How to count the number of good permutations?

This is not a duplicate and has a good answer.

Reopened

Theorems with the greatest impact on group theory as a whole (note that the question is about infinite group theory).

It is currently closed as "primarily opinion-based...Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise."

I disagree with this close reason:

1. As the 11-upvoted comment states, "This is a good question and does not deserve to be closed. Understanding the theorems that are considered most important in any field of math is an important step towards understanding that field." The theory of infinite groups is an area of active research, and is not covered specifically in an undergraduate course on groups. In fact, many results covered in undergraduate group theory are not applicable to infinite groups (Sylow's theorems are a good example, and are mentioned in the question).

2. The boiler-plate reason is that "answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise". There are currently two answers; both are based on facts and references, and both are by professional mathematicians (one is by Andrés E. Caicedo and the other is by me, and indeed my research is in infinite group theory).

Finally, I want to end with a comment: The question is almost 6 years old (5 years and 355 days, or so). The close votes here seem to have occurred after a re-tag (which I presume happened after I linked to the question elsewhere). Closing reasonably-upvoted old questions like this has the potential to discourage improvements to old question and to discourage linking to old questions.

• re 3. The question had been closed back then already. – quid Aug 19 '19 at 15:21
• I've edited 3 (it wasn't really a reason to reopen). Yes, it was closed and then it was reopened. – user1729 Aug 19 '19 at 15:23
• So, the question was already controversial back then. Which is documented by the first comment at score +12. Don't create false narratives; – quid Aug 19 '19 at 15:24
• @quid I don't see what was false about my narrative (or that I have written a narrative). My the purpose of the final paragraph (in both current and original form) was to point out the age of the question and what closing such old questions could mean. I did not mean to suggest that the question was not originally "controversial". – user1729 Aug 19 '19 at 15:30
• Further, professional mathematician or not (what type of argument is that by the way?), one of the answers does not even seem to answer the question at all. // The (at least implied) narrative is that after years were this question was welcome suddenly people took issue with the question, which is incorrect or at least incomplete. To not even mention this is careless at best. – quid Aug 19 '19 at 15:35
• People can (and should) look at the question and make up their own mind. I do not believe that it is my job here to give them all the relevant information (because what is relevant differs from person to person - for example, you focused on the close votes, but the question has only one downvote). Re "professional mathematician": my point was what I have the specific expertise to answer this question (and ignore the other answer if you wish). – user1729 Aug 19 '19 at 15:50
• It might not be your job to give all the relevant information. But I do believe that integrity ought to dictate not to give a highly biased description of the situation. – quid Aug 19 '19 at 15:57
• The above being said, I do not have a particular issue with the question itself. I'd say it still falls on the good side in the good subjective-bad subjective dichotomy, and the questioner had made an effort to steer clear of the pitfalls of the superlative. I cast the final vote to reopen. – quid Aug 19 '19 at 16:12

Undeleted, deleted, undeleted, reopened

Please consider undeleting and reopening this post: radical center of three circles.

This post clearly indicated an attempt and has a detailed answer.

Undeleted, reopened, closed, deleted, undeleted, reopened

Please consider undeleting the following question:

Is $\int_1^\infty\frac{1}{\sqrt{\Gamma(x)}}\mathrm dx$ a rational number?

I agree on the reason for closing this question. Even though the post is somewhat strange in its wording it appears to be overall interesting for the community (as the upvotes outweigh the downvotes resulting in a balance of $$+6$$). Additionally, the integral appearing in the question is strongly related to the Fransén-Robertson Constant and might be of help as future reference for this topic (as a number of relevant posts is also linked with the deleted one).

The question has got deleted again. I have still my POV listed above and I would like to hear the reason for re-deleting the question.

• I voted to undelete, but I have to say, it's a highly undermotivated question. I could write down a thousand expressions evaluating to real numbers, and ask for each, whether it's rational, without giving any reason to think it is, or any reason to be particularly interested in whether it is. – Gerry Myerson Jul 29 '19 at 23:40
• @GerryMyerson I have to agree on this issue. And indeed, the motivation is clearly missing but what remains is a relation to an actual known constant, which is from my POV the only thing which makes this question worth keeping. – mrtaurho Jul 30 '19 at 10:03
• OP has shown no interest in the question, having refused the invitation to improve it. mrtaurho, I suggest you post an improved version of the question, and your answer, so the material won't be lost. – Gerry Myerson Aug 11 '19 at 23:13
• @GerryMyerson Thank you, for your response. I will do so, as soon as I have time! :) – mrtaurho Aug 11 '19 at 23:16
• I see, mrt, that you never did get the time, which is a shame, since (as I commented on the question the other day) I don't think the main objections to the question have been addressed. – Gerry Myerson Aug 27 '19 at 0:07
• @GerryMyerson I was rather busy. Additionally, I was (and still am) rather confused what to do about this question. It has been reopened two times and so posting a new question (even an appropriate) would be in fact a duplicate. So I decided to wait for now. – mrtaurho Aug 27 '19 at 0:14

Reopened

I have edited my post “Most intuitive” average of $P$ for all $x\in A \cap [a,b]$, where $A$ is countable and the average is unique? and waited for five days. Is it clear what I am asking? If not, could any suggestions be made?

Edit:

Users are trying to delete my post. If a post is unclear why would you to delete it? This is Math Stack Exchange, not Math Overflow.

I made more edits. Is it clear now? If not please explain. Offer one hint.

If you are wondering why I have a hard time explaining my post it’s because I have not mastered the concepts needed to explain this? I don’t care if this is worthless or gold. I don’t care if anyone steals this. I just want some guidance and most of my professors are too busy.

Second Edit:

I shortened the post to one question and a couple of paragraphs.

• Rahul commented on 21 August that you had a couple of equals signs where there should have been element-of symbols. You never engaged with that correction. – Gerry Myerson Aug 30 '19 at 0:06
• @GerryMyerson Correction made. Is there anything else? – Arbuja Aug 30 '19 at 0:18
• I don't know. It's not my area, and it's long enough to be a PhD thesis. Sorry, but I won't be going through it in detail. – Gerry Myerson Aug 30 '19 at 2:32
• @GerryMyerson Users are trying to delete my post. Is this acceptable? – Arbuja Aug 30 '19 at 21:22
• As Gerry has pointed out, your post is very long. Have you thought in splitting the content and ask many questions instead of only one? – allesia_b Aug 30 '19 at 21:40
• Or you could also start a bounty :) I think you can set one for +150 – allesia_b Aug 30 '19 at 21:41
• I really don't know what to tell you. Maybe what's unclear is which of these many questions is the question: What is the "most intuitive" average of $P(x)$...? What do you think of these properties/examples? Are they reasonable? If so, how can we create a measure that suits these intuitions? And if not, how can we create a measure that suits better intuitions/intuitive examples/properties? So far, are my intuitive properties reasonable? If not, could we find the most "intuitive" Folner Sequence of any countable set? What would be the measure and average be? – Gerry Myerson Aug 30 '19 at 22:54

Undeleted, reopened

Please undelete and reopen this post:

How to show $$13\left(x^{2}+1\right)+\sqrt{2\left(x^{4}+1\right)}+62 x-\frac{45\left(x^{2}-1\right)}{\ln x}>0$$ for $$x\in(0,1)$$

Context for the question was added upon request by the asker, which has been lifted to the post.

Undeleted, reopened

Please undelete and reopen this post: How can one integrate $$\int\frac{1}{(x+1)^4(x^2+1)} dx$$?

OP wants to calculate this integral. He/she is not asking for a solution to this integral per se but states in the post his/her frustration on partial fraction decomposition (PFD) of the integrand. OP even has attempted to use something else (u-substitution) to solve this problem. Benard's answer addresses the difficulties of PFD without divulging the complete solution to OP.

Reopened

Please consider reopening Minimal surfaces under conformal parametrizations - proof verification

It appears to have been closed after the user vandalised their question (rolling back the question would seem like the better approach, which I've done) and appears to have plenty of context and be a reasonable question asking for help.

Reopened

I asked a question yesterday: Coupon collector's problem: mean and variance in number of coupons to be collected to complete a set

This asks for the mean and variance of the coupon collector's problem in the general case when the coupons have unequal probability. It has been marked as a duplicate of this one: Expected time to roll all 1 through 6 on a die

My edit clearly explains that I'm asking for the variance in the general case, while the question it is a supposed duplicate of asks only for the mean and that too in the special case of the coupons having equal probabilities.

So, the first question is not a duplicate of the one linked to it for sure. For this reason, I wanted the duplicate tag to be removed if possible.

I did ask a similar question myself in another post a few weeks ago here: Coupon collectors problem: variance calculation missing a term.

However, I wish to delete that post (the only answer there is my own) and want people to refer to this one since it is much more comprehensive.

In any case, the current question linked there is clearly more limited in scope along multiple dimensions.

• I suggest that in the interests of transparency you edit a link to your earlier question into the body of the newer question, and vice versa. – Gerry Myerson Nov 28 '19 at 21:25
• @GerryMyerson I'm going to delete the other question, so this might not be necessary. – Rohit Pandey Nov 28 '19 at 21:34

Reopened

Request to reopen Derive an atlas of Monge patches for a surface in 3D

Undeleted

I'd be glad if my question Operator characterizations of continuity and “co-continuity” was undeleted. It was automatically deteleted after one year since there were no answers, no comments and no votes. Recenly I wanted to reference the question in another answer and it was very hard to find it (see my post on Meta for more details). I think the question itself is written well enough and that it contains a useful summary.

• If the question doesn't generate some activity, then presumably it will be auto-deleted again somewhere down the track. – Gerry Myerson Feb 15 at 21:38
• @GerryMyerson Hopefully, that would happen no sooner than in one year, so there is chance to get some activity. In fact, it got an upvote after the undeletion. – user87690 Feb 15 at 22:17

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.

### Reopened

The question $\sum_{n=1}^{p-1}{\frac{1}{n}} = \frac{A_p}{B_p}$ What is $A_p$ (mod $p^2$) where $\frac{A_p}{B_p}$ is a reduced form fraction? is closed as a duplicate of Proof of Wolstenholme's theorem, but perhaps this was a bit hasty. Quoting from the OP's update:

It's been suggested that Wolstenholme's theorem can be used to finish the proof. The connection between the problem here and Wolstenholme's theorem is interesting so I will try to study Wolstenholme's theorem. However, it doesn't seem like a likely path to have taken from where I'm at in my understanding. I'm also skeptical Silverman had intended for the audience of his book to discover Wolstenholme's theorem as a lemma to proving that $$𝐴_p$$ is $$0$$ (mod $$p^2$$).

Based on this, I have added the tag to it.

Can the question be reopened?

Undeleted

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.

Undeleted, Deleted, Reopened, Undeleted

• 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.

• 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. – Xander Henderson Jul 2 at 5:06

Reopened

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.

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.

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 $$d > c > 1$$:

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

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.

• 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. – Carl Mummert Oct 28 '18 at 16:19
• @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? – Calum Gilhooley Oct 28 '18 at 16:28
• @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.) – Calum Gilhooley Oct 28 '18 at 16:34
• !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. – Carl Mummert Oct 28 '18 at 21:19
• I think my guilty conscience over this has now been assuaged. :) – Calum Gilhooley Oct 29 '18 at 0:36

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.

• 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. – quid May 9 '19 at 6:59
• 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.) – Martin Sleziak May 9 '19 at 6:59
• @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. – Q the Platypus May 9 '19 at 23:32
• 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. – quid May 10 '19 at 9:55
• Fortunately similar information is available in other and better threads. In my opinion, the site is quite simply better without this thread. – quid May 10 '19 at 9:57

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.

• 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. – Arnaud D. Jun 28 '19 at 13:48
• 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). – hardmath Jun 30 '19 at 19:45
• 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. – Xander Henderson Jun 30 '19 at 23:51
• "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". – Jack Jul 1 '19 at 1:47