@amWhy : no issues at all. I can understand that such things can happen when one is going through review queues. One of the answerers had in fact voted for reopen and that's how it landed in your reopen queue. I have also asked that answerer for feedback. Let's wait for their feedback before we can take some action.
@D.Thomine: your observations are correct. However the complexity of the question is reduced once the big exponent 2021 is replaced by a symbol $k$ (I mentioned this in the comment to question).
@amWhy: maybe editing tags doesn't allow dupe hammer, but editing tags may help in earning silver and gold badges. I don't need to explain as we are not supposed to teach gaming the system, but I think this loophole is difficult to fix
I have just posted an answer here, only because I think the current answer is too short to be really helpful. But I don't mind the question being closed and deleted because honestly there is no lasting value to a convoluted hiding of a hidden assumption of 0^0 = 1 in order to prove 0^0 = 1... If you all agree then I'll cast my close/delete-votes later. Thanks!
@user21820 For one, I'm not even convinced with the identity on the first line, all that tetration and all, I'm not even sure how much it'd hold for any $x,n$, perhaps a mistake is present. Is there a reference for that identity?
Happy birthday ANDREW WILES. Expect some posts on FLT today.
@TeresaLisbon: So do you agree with my judgement that it should be closed and deleted? I haven't cast my vote because I wanted to hear from others first since I answered it.
@user21820 Very much agree. I believe I have voted to close and downvoted as well.
(Oh ,ok, I've done it now, I thought I'd surely done it earlier)
@user21820 I see you've got a downvote as well. Perhaps this is because either someone doesn't agree, or that question wasn't clear enough to get an answer, but either way we'll get rid of what's happened there.
@user21820 Fair enough, it is an odd one. I'd say you delete your answer. A certain user will remember once when they answered and voted to close a question, what furore there was! So I think you should delete it.
(There was a meta post created, lots of apologies, people saying it should have been done, not been done, ridiculous, a rainbow of opinions rose over the drenched meta post)
@TeresaLisbon I think there's no need; I explained exactly my position in a comment. If people who cannot accept it, it's their problem. After all, I'm not closing to prevent other people from being able to answer. Rather, I'm closing for the purpose of eventual deletion, which will also delete my answer.
Neither the ordinal numbers , like $\omega$ , nor hyperreal numbers are "$\infty$". It is weird that so many users do not get the difference.
re-open voted despite of an awful layout. The title was already edited (unreadable befor this) , but the question belongs in the body and also the attempt.
@Peter It's a difficult poster, I think a short comment culture akin to WhatsApp is present, so I will try but I expect to back off. You can take a look, I've really tried hard.
@TeresaLisbon True, the user is not cooperative. But before to post hints, this post must be repaired. It will be much work, I know, but before someone did that, we cannot reasonably continue.
Additionally, the question is far from easy, but this is another story.
@Peter I am planning to clean up the user's English and MathJax. I won't put a stamp on it, but I will capitalize and space things out. I think the user is going about editing their question right now, and I hope that things work out.
@Peter The definition of spam on the SE network is very limited. It refers to comments or posts which advertise a product or service without disclosing the author's affiliation. In this case, the author was up front about their affiliation. While I am not the moderator who handled your flag, I probably would have done the same thing.
Please see if this is now worth reopening. I believe the user has a language issue that has lead to miscommunication. Please note that I have edited it in accordance with keeping everything basic and simple to understand. Kindly check, thank you
(Going out for half an hour, I won't respond for this reason, thank you)
@Peter In my opinion it's not spam, because "spam" is reserved for unsolicited junk/marketing and this link is really to a mathematical blog post with no monetary strings attached. However, the question is completely opinion-based, so it ought to be closed. For the record, I just want to say that I don't recommend that blog post because it is wrong about PA. Too many people think that the original axioms Peano devised are correct. Technically, they aren't.
That said, Xander has given you the SE definition of "spam", which is even more restricted than mine.
@Prithubiswas (1) it is very long, (2) it is not clear what your actual question is, and (3) at the end, you seem to be asking at least five questions.
2
I would suggest trying to edit the question so that the actually question is clearly and narrowly defined right at the beginning ("Is my proof correct?" is not a narrow question). If you have a specific doubt about the correctness of your argument, please try to highlight that specific problem.
In general, "spot the error" questions are not really a very good fit for Math SE. Yes, the solution-verification exists, but it is intended to label questions in which the asker is concerned about a specific step.
@XanderHenderson Another thing , the question is not just about a proof of mine , but the main reason why I tried to do the proof is it was about a paragraph of the book.I will be needing the paragraph thoughout many parts of the exercises , so it was important I would try to understand what it meant.
The first time I asked about this paragraph , it also got downvoted (for no effort I guess).I also think the question wasn't useful for me , so here is my second post that I showed here.
First post https://math.stackexchange.com/questions/4089985/extension-of-proposition-2-4-2-7-in-mendelson-logic second post https://math.stackexchange.com/questions/4095524/technique-for-applying-deduction-multiple-times-in-mendelson-logic
@Prithubiswas Most probably the close-votes were when your question was in a bad state where all you said was "I was unable to understand this paragraph at all." without specifying what about it you didn't get.
In the current form, it's far less likely to get closed, and you can always try to reopen it if it does.
As for your second post, reposting just because a previous version was not well accepted is not acceptable on SE.
You're supposed to edit and then request reopening.
Maybe I should just check the proof myself.It will take some time but writing in a pen and paper takes far less effort for me than to write an entire post with that proof. :)
Oh sorry , I thought you said down votes .My bad. Also I did not get any close votes (Probably I will get soon.time will tell).
@Prithubiswas Oh maybe you cannot see close-votes. I can. It has some right now. They will disappear if your question survives long enough. Your goal should be to post a question of good quality from the beginning, to avoid downvotes. Try to make your questions clear and concise. Include context (such as your own efforts), but don't ramble.
@user21820 Hey, thanks for the comment on this post. I hope the author responds and continues, actually I kind of semi-hope that they won't finish the question, because I intended to keep the inequality like that to scare them a little.
Although my hopes are fading of the user returning, I still lie in wait. This could go down as a failure.
@user21820 My final thoughts are,the question is concise enough , but it is asking for too much , as @XanderHenderson said "In general, "spot the error" questions are not really a very good fit for Math SE".I will think about my proof tomorrow again with pen and paper. I am out.
@Prithubiswas Concise means you need to be able to pinpoint quickly and accurately what you are unsure about. That is precisely why Xander says "spot the error" questions are not a good fit for SE. This is not a Find Waldo website.
I can confirm that the wear and tear of the reopening here did not go to plan. I probably gave away a little too much , although I was conscious of trying to keep the focus on the overall editing the mathematics still got to me, the last couple of comments divulged too much. I'm hoping to learn from this.
When you hover over the up-triangle to the left of a question, does anyone see, "if you answer a question, upvote it"? I don't see anything of the sort. But it is clear enough to hypothesize that the number of upvotes on a PSQ correlates closely with the number of answerers who chose to answer the PSQ. :(
@XanderHenderson And, in all fairness, my hypothesis is about a correlation between PSQ's upvotes, and number of PSQ answerer. So your data is irrelvent to they hypothesis! ;P
@amWhy No, I am just pointing out that I think that anyone who bothers to answer a question should believe that the question is worth answering. Upon reading your subsequent comments, I think that you are pointing out an orthogonal issue, i.e. only the answerers of PSQs think them worth upvoting.
I've also noted a pattern of "cohesion" of PSQ answerers supporting PSQ answerers, through upvotes. Particularly so on meta posts. So I really don't get the singling out of CURED.
@amWhy I mean, like minded people are likely to support each other. It is troublesome to me that there are people who are so supportive of PSQs, but it is not surprising to me that they upvote each other.
@XanderHenderson I agree, it is not surprising; but they are hypocritical in condemning CURED for their actions, which are discussed openly, publicly, before taking action. That was my point. In fact I'll make it if I ever encounter more scolding in this room from a mod who shall not at this time, be named!
@Xander, @Paramanand, at others: Would it be fair to consider the issue of "the answering of PSQ's" as the primary division between users and between mods? Or does that division include even the issue of "the asking PSQ"? Or am I missing something bigger?
@amWhy I would agree that one of the most divisive issue on Math SE right now is the handling of PSQs. This seems to stem from a disagreement about the purpose of the site (tutoring vs building a repository).
@XanderHenderson Yes, but even as a proponent of tutoring centers, it is never effective in tutoring to to a student's homework for them. I spent three years supervising the training of tutors, with a strong emphasis on hints, or going through a similar question with them, and supervising their work on their question at hand.
Completing others homework, test questions, etc., is not what tutors or teachers or professors do, unless the tutor or test examiner/test evaluator is part of a huge ring, Like Singer's, where parents pay for the cheating on behalf of their kids.
As for the archive, we need to seek the best answer to the best questions, all in one. Or merge a good answer to a poor question, with a far better question.
But for many users, the issue of seeking non-deletion of PSQs directly impacts their ability to secure rep so quickly than warranted, fearing a stricter policy on answering PSQs will leave them in a desert of questions they can answer.
@XanderHenderson I'm not stating all this to convince you ;D But I appreciate we are of similar minds. But I have yet to see a mod defending PSQ answerers, or a user ranting on meta about a deleted question which also deleted their run of the mill answer, but in their eyes, an example of excellence, who is able and willing to sit down and discuss these issues.
@Xander, if you have not yet gotten groceries, please feel free to go, for now. But pick me up a six pack, while you're at it! ;D
@XanderHenderson No problem! (Yet another Xanderism we will add to our collection of Xanderisms). Their cute, because it's always clear what you mean, save for the fact that you dissed the Matrix Trilogy!
I don't think that this question is necessarily poor enough to merit immediate closing, but I am having a little trouble understanding what the asker is asking for.
Perhaps someone with a better recall of basic algebra could help them out?
Like, I remember that the Sylow Theorems are a thing, but it has been a decade since I've thought about them (I think that the answer probably has something to do with Sylow subgroups, maybe?).
@XanderHenderson I get infuriated when a one-sentence PSQ enters the "reopen review queue" and clicking on "leave closed" renders an audit failure, because the question earned 5 upvotes and has six answers, and weirder still, no close votes. Ugh!
@XanderHenderson I understand. And you had a great point. I was one of the close voters, but not a deleter, nor did I downvote. I'd be willing to cast an undelete vote, hoping at least to get it undeleted, then improved.
Done, I voted accordingly.
@XanderHenderson It's ironic that this site eventually forces regular participants to acquire proficiency in Conservation of Resources, lest they go insane. First and foremost, likely, it applies to mods of this site.
But, @Xander At the same time, anyone whose earned a PhD and is teaching comes prepared, and I imagine adding the duty of moderation of site, with no compensation, is the ultimate test!
@amWhy Generally speaking, failing an audit because I have voted to close doesn't take much time. I just get annoyed.
In the case of the question I mentioned above (which had already been deleted), I spent some time Googling, came in here and asked for advice, and started writing a comment. I probably spent 5 minutes on the question, which it was an audit I should have simply voted to close. :(
@XanderHenderson Oh, yes, I get it, but again, I was speaking more generally in my comment about acquiring profiiciency in conserving one's energy on maintaining this site in general, of which review queues are a small part.
Did anyone have dummit and foote chapter 14 solutions
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