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Why does $n = \lceil 1/\sqrt{x-1}\rceil+1 $ imply that $\frac{1}{n^2} < x-1$?

Since this clearly doesn't require any complex 'context', the only reason I can think of for it getting closed is that there was no effort shown. However, I believe no such rule is observed in this site since I regularly see questions with no attempt upvoted to high heaven. So, why was the question closed? I don't particularly care for it getting closed, since it served its purpose for me, and I had accepted an answer way before it got closed. I'm just trying to understand how this site works!

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    $\begingroup$ Here is something missing in terms of context: "Why does ... imply ..." contains the presupposition that the implication holds. How do you know this if you can't prove it? There are of course also all the things explicitly mentioned under the closure reason... $\endgroup$ – Michael Greinecker Dec 3 '17 at 21:43
  • $\begingroup$ See also: Homework, reasonable to have no clue? $\endgroup$ – Simply Beautiful Art Dec 3 '17 at 22:00
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    $\begingroup$ Whether a question with no effort gets closed or upvoted depends on who sees it first. m.se is a big website, and its users are not all of one mind. The closers have the upper hand, but occasionally something gets past them. $\endgroup$ – Gerry Myerson Dec 3 '17 at 22:08
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    $\begingroup$ That's not why I linked it. Being basic does not make a question exempt from the bullet points in the answer in the link above. $\endgroup$ – Simply Beautiful Art Dec 3 '17 at 22:27
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    $\begingroup$ It's a random problem. If it's connected to something else, mentioning it would provide motivation as well as indicate where it came from. These points probably make up for the context which your question lacks in your mentioned "questions with no attempt upvoted to high heaven." Seriously though, asking questions like this is generally considered rude. $\endgroup$ – Simply Beautiful Art Dec 3 '17 at 22:38
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    $\begingroup$ "In what possible way would the question or the answer given be improved by the fact that it was from the proof that a sequence was convergent, for example? " The thread would seem more interesting to me. Moreover, all this is spelled out in quite some detail in the thread I linked too. Plus there is Michael's point that you so far chose to ignore. $\endgroup$ – quid Dec 3 '17 at 22:52
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    $\begingroup$ And false equivalence or not, I don't see how your behavior is any better than what Hurkyl has described in his comment. $\endgroup$ – Simply Beautiful Art Dec 3 '17 at 23:19
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    $\begingroup$ If someone is ticketed for speeding, e.g., then claiming that they've seen other people speeding that didn't get caught, why can't they get away with it, too, has nothing to do with the fact that you were speeding. And those caught speeding are subject to a ticket. $\endgroup$ – Namaste Dec 3 '17 at 23:29
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    $\begingroup$ @amWhy Surely, the question raised by the person given the ticket is meaningful when the said person has seen the same people giving out the speeding tickets not only letting others get away with it, but partaking in the offence with them too (what I said earlier about people who vote to close one question missing context partaking in other questions similarly missing context)? I mean, of course it won't set aside the ticket, but the person is right to question the inconsistency. $\endgroup$ – Alt-Rock Dec 3 '17 at 23:43
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    $\begingroup$ @amWhy I'm calm, thank you! Your analogy wasn't sound. I was simply illustrating that. I find it ironic that you patronise me by saying "read more than your own grandstanding" yet your "reading" failed you where I said closers (police, in the analogy) partake in the supposed offence themselves. $\endgroup$ – Alt-Rock Dec 4 '17 at 0:07
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    $\begingroup$ See the bolded part of the missing context message: "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." Seems pretty clear to me. $\endgroup$ – Qudit Dec 4 '17 at 0:08
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    $\begingroup$ @SimplyBeautifulArt I went through your answers to see if you practice what you preach. You have happily responded to dozens of questions with no effort and/or context with no qualms. Didn't you find it rude? I mean, wasn't it the same as them walking into your office, placing their homework sheet in front of you, and silently waiting for you to give the answer? No? $\endgroup$ – Alt-Rock Dec 4 '17 at 0:15
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    $\begingroup$ @Alt-Rock I'm not sure what offense you are saying these closers committed. If you are saying they let other questions go, then realize that you are speaking to someone who holds third most close vote reviews, and I myself have cast 15 hundred close votes as well. The only things that hold us back are the fact that we cannot go through every question on our own and that there is a limit to the amount of 'tickets' we are allowed to hand out each day. $\endgroup$ – Simply Beautiful Art Dec 4 '17 at 0:16
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    $\begingroup$ @Alt-Rock I make mistakes, and I try to fix them. I'll also admit that my opinions of this site have changed over time. $\endgroup$ – Simply Beautiful Art Dec 4 '17 at 0:19
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    $\begingroup$ One thing that this post has accomplished is the ability to link to it when there is conflict about when and when not to answer a question, for it reflects precisely the concern of many of us: Irresponsible answerers and upvoters of poor, effortless, PSQs, do, in fact, lead other users, like we see here, complain because he "did what he saw, and thought it was okay then." So the confusion here is not due to the fact that some users can't be here at all times (dah!), it's a problem of apathy, and downright ignoring of the need for the community as a whole to not model, what this user sees. $\endgroup$ – Namaste Dec 4 '17 at 19:37
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The banner indicating that the question was put on hold for lack of context contains a link to the following question

How to ask a good question.

Among other things it contains a detailed discussion of various forms of context. The discussion contains six bullet points.

The following two seems especially relevant to me given your question.

  • You can provide some motivation to your question.

Instead of just asking us to find the roots of an equation, tell us where the equation comes from.[...]

  • You can tell us where the question comes from.

If your question comes from studying a textbook, let us know which book.[...]

The question as is seems a rather unmotivated. I can understand it but I do not see why one would care about it.

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    $\begingroup$ 1. Does this only apply to low level questions where context might not even be necessary (as you said, you understand it, though you may not particularly care for it). I mean, is this rule actually observed? Because as I've stated, I've seen so many much more involved questions with no demonstrated effort voted into the multiple digits, and they don't get closed. 2. What's the utility of closing a clear question long after it had an accepted answer? $\endgroup$ – Alt-Rock Dec 3 '17 at 22:07
  • $\begingroup$ @Alt-Rock You seem to say that you see a lot of low-quality questions. You should flag them as off-topic/missing context (when you believe appropriate of course) $\endgroup$ – Simply Beautiful Art Dec 3 '17 at 22:41
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    $\begingroup$ @Alt-Rock re 1. No. But in practice more advanced questions or those that seems to have some intrinsic motivation can fare well even without contxt. I wrote about this in more detail earlier (also see the other contributions) But also it is not a given. Moreover, given that the site is community moderate it is to be expected that there is some variation. re 2. If we do not close it user Synth-Pop will ask a similar question next year and will then upon closure come to meta and quiz us how it can be that that question of Alt-Rock was not closed. $\endgroup$ – quid Dec 3 '17 at 22:47
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    $\begingroup$ +1 for "The question as is seems a rather unmotivated. I can understand it but I do not see why one would care about it." I happened upon this meta thread, and that was my first thought when I saw the question (within the question). For a few seconds I thought it might be something that arises in estimating something for large values of $n,$ but then I realized the conclusion is weaker when $n$ is large. Finally, I figured it was just some random math contest-like problem someone came up with, which is fine, but we should be told the origin of the problem (to the extent the OP knows this). $\endgroup$ – Dave L. Renfro Dec 4 '17 at 15:15
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    $\begingroup$ @Alt-Rock Any thing stated exactly or almost exactly like a text-book exercise, an assignment sheet, *with no additional information and/or no participation from the asker, comes across to me as being a "do-my-work-for-me" question, whether it's a basic algebra problem statement, or it comes from say, algebraic topology. So I'm very consistent in my expectations, across the board of "levels of math". Yes, when I do downvote, or vote to close, it's usually (almost always) a vote given to a an asker who simply posts a question only, and waits for us to do it for them. $\endgroup$ – Namaste Dec 4 '17 at 19:55
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    $\begingroup$ @amWhy I completely understand that. However, what boggles my mind is the attitude that these type of questions are rude while at the same time happily indulging these type of questions. I completely understand that an effort is required, and that context is necessary of course, and all of your comments here make complete sense to me. It's just that there are certain double standards from some of the very same users who were calling my question rude. $\endgroup$ – Alt-Rock Dec 5 '17 at 2:45
  • $\begingroup$ I'm not calling your question rude; But/and it might be a bit rude to cluster all questions missing context under the umbrella "rude". You raise a good question/observations that this site is indeed inconsistent in dealing with "PSQ's", and of course, the inconsistency is ultimately to the users of this site (at least some of them.) That's not an excuse, only a confirmation that the some users expect you to "do as I say, and not as I do", some are sincerely looking after the site and trying to maintain the quality of this site,... $\endgroup$ – Namaste Dec 7 '17 at 23:39
  • $\begingroup$ Alt-Rock (cont.) from above comment.... And some of us have matured from one stance to the other, over time, so that is a point to consider. But yes, I'm afraid this site has "double" (even n-able) standards, and that's unfortunate. $\endgroup$ – Namaste Dec 7 '17 at 23:45

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