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(Yes, I realize that this might be very obviously argumentative, but hopefully some response here will help understanding in how to deal with other 'meta' questions)

Hypothesis: Any question that is stated in the imperative, e.g. "Prove that..." "Show...", is homework whether tagged or not.

For:

  • if a question were not from another text, then any normal person would not word a question with the imperative ever.
  • most people (here?) are normal
  • so it is from another text, cut and paste or copied closely from another text.
  • there are two (primary, not necessarily independent) reasons for copying from another text: one, since there is a question about it, possibly the wording, one needs to preserve the original to get the appropriate answer; two, because one is lazy.
  • people who would ask a site like this for help on homework are probably lazy. Therefore, it is most likely that a person asking in the imperative is probably asking for help on homework.

Against:

  • Given some of the explanation above, cut and paste is not so necessarily homework. People very reasonably can read a text not for a class, trying to do the exercises. And the best way to relate an exercise is verbatim (because the problem may be with the statement of the exercise).
  • What's been typed and entered into a question box here is a pinhole camera onto the mind and intentions of the OP, it is impossible to second guess the intentions of the writer, and it's more robust to simply take things written at face value (that the imperative is simply unintended rudeness).

I don't have very good 'against' items because I am so convinced of 'for'.

I am fully aware that some people have been politely using the homework tags (but I'm sure most people omit tags not out of malice or but lack of knowledge, but then I'm sure they wouldn't bother with the tag if they knew).

So the question here then (to make a question out of it) is...do you find imperative mode to indicate homework? (and give your reasons either way)?

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    $\begingroup$ I've cast the second vote to close as "subjective and argumentative". I don't see a way to answer this question objectively. Asking about a question being homework out of one's presumptions on the questioner, may lead to funny situations, see e.g. here. $\endgroup$ – t.b. Apr 25 '11 at 8:55
  • $\begingroup$ Nothing funny about this. 70 year old students exist although they tend to be quite mature and diligent. $\endgroup$ – Phira Apr 25 '11 at 9:48
  • $\begingroup$ @user9325: Nobody claimed they didn't exist (I had a classmate of 75 when I started studying). The rebuttal in itself is funny to me, but that of course is in the eye of the beholder. (This was only meant as an aside and probably should have been posted separately, if at all since not relevant to the discussion). $\endgroup$ – t.b. Apr 25 '11 at 9:54
  • $\begingroup$ I had cast the third vote, as Theo's word managed to convince me to do so. $\endgroup$ – Asaf Karagila Apr 25 '11 at 9:55
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    $\begingroup$ @Theo, Asaf: This is a genuine question: isn't the point of the meta site exactly to allow people to discuss issues relating to the site and to express subjective or argumentative opinions as long as they are constructive? It's not as if this is the main site; we are just stuck with using the SE interface for discussion here instead of a proper forum. $\endgroup$ – Carl Mummert Apr 25 '11 at 12:14
  • $\begingroup$ @Carl: Come to think of it, it seems to me that you're absolutely right. Thanks for pointing that out. $\endgroup$ – t.b. Apr 25 '11 at 12:23
  • $\begingroup$ @Theo I agree with Carl and as such I've cast the first vote to reopen. Let's see how well reopening works these days... $\endgroup$ – Bill Dubuque Apr 25 '11 at 19:28
  • $\begingroup$ @Bill: Ok, let's try. $\endgroup$ – t.b. Apr 25 '11 at 19:32
  • $\begingroup$ @Theo: would it be weird for me to vote to reopen? Should I recuse myself? $\endgroup$ – Mitch Apr 25 '11 at 19:36
  • $\begingroup$ @Mitch: Probably your recusal would be more appropriate than voting (but see Bill's comment below). Out of curiosity: Do you really have the option to vote to reopen? What happens if you click on reopen (I get a dialog where I can still click cancel)? $\endgroup$ – t.b. Apr 25 '11 at 19:45
  • $\begingroup$ @Mitch Presumably you are allowed to vote however you wish. I see nothing weird about it. Though this thread could be "argumentative" it isn't yet and, considering recent circumstances, I think it should be allowed so that folks can see the wide variety of opinions on such matters. This may help folks to choose better ways to deal with poorly posed question - or at least ways that don't alienate other folks. $\endgroup$ – Bill Dubuque Apr 25 '11 at 19:47
  • $\begingroup$ @Theo: On clicking 'Reopen (3)', I get a dialog with OK or cancel for "Nominate this question for reopening?". Which seems weird. $\endgroup$ – Mitch Apr 25 '11 at 19:49
  • $\begingroup$ @Mitch: Thanks for the information. So I guess if you have the option, nothing prevents you from casting your vote (the (3) stands for there are already three votes to reopen). $\endgroup$ – t.b. Apr 25 '11 at 19:51
  • $\begingroup$ @Bill: - I agree with you, but I see the reason for closing, but I also see Carl's point. I won't vote even though I am an interested party, and technically I want to see how questions get reopened. $\endgroup$ – Mitch Apr 25 '11 at 19:53
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    $\begingroup$ So, should I wait for it to be reopened before posting my answer, or should I post it as comments to another answer? I think this question is exactly the sort of thing people should be discussing on meta, because otherwise the alleged "community norms" regarding closing have nothing to do with community. $\endgroup$ – Matt Apr 25 '11 at 20:04
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One thought that occurred to me, coming across so many posts by users who are frustrated by the use of the "imperative" in questions: It is often the case that when speaking (writing) in a language which one has acquired (e.g. English as a second language), that verb tenses and forms are a bit off. In fact, the most common error is to use the declarative or imperative by default, particularly since English is a rather idiosyncratic language (with more exceptions to rules than rules themselves!) So, it is not at all surprising to me that we may come across frequent use of the imperative. "You go the the store?" vs "are you going to the store." etc. I know when I first learned Spanish many years ago, I could speak most fluently in the imperative: conjugating verbs, applying different tenses, etc, all took more time.

It's also a possibility that, when presenting a question in a post, OPs are modeling precisely how they've learned math questions are posed! That is, their experience with "good math questions" comes largely from how they've been asked questions: textbooks, tests, homework, theorems: almost without exception, use the declarative or imperative.

It does bother me how so many users here are so quick to judge the motives/motivation of OPs when they've posted questions; indeed, as admitted in the opening question, a good number of folks here have made up their minds/are convinced (perhaps not open to reconsidering?) their positions. Can I ask: Was this question asked with sincerity? (Regarding consideration of your "theory" that imperative implies homework?). Or have you made up your mind?

One possible solution might be this: if you're skeptical about a question being homework, and the OP hasn't tagged it as "homework", and you're convinced it is, you are free to not answer it. No one is forced to answer a given question. Ignore it. You're entitled to your evaluation of the merits of the question, and you are free to determine how to spend your time here. But please grant all users that same entitlement. There may never be a consensus about what constitutes homework, or how to approach such questions. Perhaps we can agree to disagree, and agree that each of us is entitled to his/her own perceptions and decisions about whether to answer, and/or which questions to answer and how best to answer them.

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    $\begingroup$ Re last paragraph: it's not quite so simple. There are several lecturers here who see questions that they posed on the exercise sheets being asked verbatim in the forums. Some of these exercise sheets contribute to the degree grades. In any case, the students' performance on the exercises is supposed to give the lecturer an idea of their progress and to help pitch the pace of the lectures correctly. So, just saying "oh, it's the hw I set, so I won't answer it and will let someone else answer it" is a pretty frustrating option for a lecturer, and does not help the student in the long run. $\endgroup$ – Alex B. Apr 25 '11 at 9:35
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    $\begingroup$ "In fact, the most common error is to use the declarative or imperative by default". (I disagree, but this is off-topic). I disagree with the relevance of second languages for imperatives, and your example "You go to the store?" is has nothing to do with imperatives. Do you really contest the assessment that "Make and prove a conjecture on ...." is not a question formulated by the person posting it here? Some formulations only make sense if you know the answer and assign the problem as an exercice. This has nothing to do with foreign languages. $\endgroup$ – Phira Apr 25 '11 at 9:40
  • $\begingroup$ Re: "You are free not to answer it" - of course. For me, it is very easy to read an interesting question "show that..." and go into problem solving mode, only to naively realize later that such a wording is kind of strange especially without some sort of additional questioning "what does this mean?" or "how do I do this?" SO I find the question interesting, have solved it in my own head, bu then realize I might be doing somebody's work for them (and encouraging plagiarism). What to do? It is very frustrating. $\endgroup$ – Mitch Apr 25 '11 at 14:20
  • $\begingroup$ Re: "sincerity" - I am being honest. When I see the imperative (in a short presentation by someone who responds very curtly or not at all), I interpret that as asking for an answer to homework. I have my doubts (I am sure it is not always the case), but I highly suspect that it is the great majority of the time. But because of my doubts, I'm trying to find out other points of view.... $\endgroup$ – Mitch Apr 25 '11 at 14:25
  • $\begingroup$ con't'd... Again to be honest, the point of view which takes the question statement literally (as an actual imperative 'do it') I find is misunderstanding the situation, too literal minded of those who complain about it. Or maybe -I'm- being too literal and those who complain about the imperative are really thing it is a homework statement but treating the questioner in a manner to get out of simple cut and paste and to start thinking about the problem. $\endgroup$ – Mitch Apr 25 '11 at 14:27
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I asked my first question here in the imperative. I am not sure why I crafted it to look like a homework problem; it certainly didn't come out of a textbook. English is my first language, and I'd been lurking for a while before posting, but somehow it didn't occur to me that my wording was inappropriate. It stands out to me as strange now, but it clearly didn't initially. I just looked in the FAQ and didn't notice a suggestion to not use the imperative, although I seem to recall seeing it before.

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    $\begingroup$ That's the kind of things I'm looking for. I don't want to jump to conclusions always. (but then looking at that particular question, you certainly followed up your imperative question with a very reasonable explanation of your thoughts on the subject, which whether homework or not, is a good thing to do that you naturally did. $\endgroup$ – Mitch Apr 25 '11 at 14:12
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Part of the linguistic tradition of mathematics is asking questions in the imperative, and asking them as concisely as possible.

This is like the tradition of using "we" in answers (which is not the royal "we", but rather meant to include the reader who is assumed to be participating) and making them as concise, precise, and clear as possible.

If I am telling friends my latest math question, I will say something like:

Prove that the expected number of points that need to be placed (randomly) on an n-sphere until their convex hull includes the center is 2n+3.

or

Aliens get dropped one by one at random locations on an n-dimensional planet. They capture it when their convex hull includes the center. Show that the expected number of aliens needed for capturing the planet is 2n+1.

I will not say something like:

I have been working on the following problem: [describe alien problem] The case n=1 is easy, but n=2 was difficult and required evaluating a series of series of series, and I can't imagine how to approach n=3 because it seems to depend on the geometrical arrangement of the aliens dropped so far in a way that cannot be parameterized by a finite set of parameters. Does anybody have an idea how to approach this?

I also would not want to hear this third one. I much prefer the first or second.

There is only one situation in which I prefer to hear the third one: If it is homework.

The reason I want to hear it then is because it is their homework, not mine, and I am strongly against rewarding laziness with free help. But this has nothing to do with the mathematics of it.

Using the imperative does not imply homework. For example, I asked this question in the imperative, as concisely as possible. (Perhaps too concisely for Willie.) I like it the way I asked it, and I see nothing strange about how it was phrased. In fact, it was edited several times, but nobody changed it from being concise and in the imperative.

So, to answer the original question: No. A question being in the imperative does not imply that it is homework. The first bullet point under "For:" (from which all the other bullets follow) is a false premise.

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    $\begingroup$ First, let me note that I do see your point and that I don't have any particularly strong feelings about there being a connection between the phrasing of the question and whether or not it's homework. That aside, I'd draw a technical distinction between "posing a [mathematical] problem" and "asking a question." Your first two examples are nicely-posed problems, but there is no question in either of them. Your third example would, as you say, be a rather messy way to pose a problem, but it actually does ask a question. I am inclined to think that $\text{Q&A}\neq\text{problem & solution}$. $\endgroup$ – Isaac Apr 26 '11 at 12:35
  • $\begingroup$ @Isaac: I don't see the distinction between question and problem. I also don't see the import. Also I don't get the last line Q&A!= problem&solution. Can you clarify? $\endgroup$ – Mitch Apr 26 '11 at 17:58
  • $\begingroup$ The question I linked to towards the bottom of my answer was indeed a question. I had been wondering about it for a long time, ever since I heard it (as a question, like "how would you prove that?") from a friend. Mathematicians (or maybe just certain subfields? but certainly not just me) like to pose questions as problems to be solved. I think this has no bearing on their appropriateness for the site. $\endgroup$ – Matt Apr 26 '11 at 17:58
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    $\begingroup$ I have explicitly avoided talking about dislike of homework questions in my answer, since that is not part of the question. Just to be clear: Yes, I dislike being asked to do other people's homework. Yes, it bothers me that some students are not trying to understand the material but are hoping to get something they can hand in, and m.se helps them. Yes, I have seen questions on m.se that are not marked as homework but look like homework to me. Yes, the imperative tense feels like part of the clue. But: I think this is because book authors tend to phrase questions as a good mathematician does! $\endgroup$ – Matt Apr 26 '11 at 18:07
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    $\begingroup$ @Matt: Your answer is what I was looking for on the other side. Whatever the real distribution I think it is safe to say that imperative by itself does not imply with high probability cut&paste or homework. I understand your method and it is reasonable but I do not share it (I would balk, like others, at the imperative as presumptuous, even though it is pleasantly efficient). In fact, If I were able to get tot the point of stating such a thing so clearly, I feel I would probably have followed a path of understanding to a point where I would have solved the problem already. $\endgroup$ – Mitch Apr 26 '11 at 18:12
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    $\begingroup$ @Matt: I agree that answering whether imperative = homework does not answer whether homework is identifiable without the tag or if homework questions (marked or unmarked) are appropriate. I think extra info helps to identify hw, like commentary by the OP, rep points, interaction (well, this whther hw or not is just welcome anyway). $\endgroup$ – Mitch Apr 26 '11 at 18:20
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    $\begingroup$ @Matt: From Wikipedia: "A question may be either a linguistic expression used to make a request for information, or else the request itself made by such an expression. This information is provided with an answer." That is, a question is a request for information. A problem statement is a command to do something. StackExchange sites are question and answer (Q&A) sites. I'm claiming that Q&A is not the same as posing problems and collecting solutions. It is important that there be some specific answerable question asked. $\endgroup$ – Isaac Apr 27 '11 at 1:09
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    $\begingroup$ @Isaac: Are you saying that "Show that..." is asking for different information than "Can you show that..."? If we're taking things so literally, the first is a directive and the second is actually asking for a Boolean value. But in the real world, these are neither a directive nor a request for a Boolean. They mean exactly the same thing, regardless of one being phrased as a question. $\endgroup$ – Matt Apr 27 '11 at 6:30
  • $\begingroup$ In practice, question askers have problems they can't solve, and answerers provide solutions to those problems. This is true not just on m.se, but on stack overflow, yahoo answers, or wherever. It seems to me that in general Q&A==problem&solution. One exception would be cases where the asker is requesting a specific piece of information rather than a solution to a problem ("Who proved the Poincaré conjecture?"). But that's what Wikipedia is for. Are there other exceptions that I'm missing? One of the main points of a site like this is to provide solutions or hints to math problems, is it not? $\endgroup$ – Matt Apr 27 '11 at 6:54
  • $\begingroup$ @Matt: I did say it was a technical point, but I think it's an important one. Both "Show that..." and "Can you show that..." are lousy questions here. "How can I show that..." and "How would you show that..." are much more interesting questions (and subtly but importantly different). I can't imagine going up to a friend or into a professor's office hours and saying "Show that..." or "Can you show that..."—saying "How do I..." is much more sensible. And, specifically, I don't think one of the main points of a site like this is to provide solutions; it's to answer questions. $\endgroup$ – Isaac Apr 28 '11 at 0:32
  • $\begingroup$ @Isaac: It seems we agree more than we thought at first. I also think "Show that..." would be strange for office hours. For a friend, I wouldn't start with "Show that...", but rather with "Here's a nice math problem: Show that...". The phrasings you prefer sound to me like asking for help with homework (perhaps self-assigned by an auto-didact). The phrasings I prefer sound to me like offering a treat. Of the 3 formulations in my answer, #2 looks like a tasty treat to me, while #3 looks like helping someone out of the mud, which I'll do if I can, but it's not as tasty. Everyone's different! $\endgroup$ – Matt May 30 '11 at 18:17
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  • It certainly indicates that this is homework, but in the recently discussed cases where I brought in the question/tag, there were additional indications.

  • A question could be posed in the imperative because a young poster thinks that this is the way mathematics questions are posed, but in that case, noone stops them from explaining their background when asked.

  • People can be as lazy as they want. What I dislike is dishonesty and entitlement. And being told that "we" are obligated to answer any question. No, I am not obligated to do so, especially, if the asker does not interact.

Personally, the recent polite question starting with "Sir" annoys me as much as a question starting in the imperative, and certainly less than "we" language and moral adjectives in a discussion on policy.

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    $\begingroup$ See my post above. The use of "Sir" and other such titles is often a cultural norm (certainly not for much of the US!), but among some minority communities and other cultures world-wide, deference (particularly to "authorities") is the order of the day. $\endgroup$ – Namaste Apr 25 '11 at 9:15
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    $\begingroup$ @Amy It annoys me because I am female, not because it is deferential. $\endgroup$ – Phira Apr 25 '11 at 9:19
  • $\begingroup$ I hear you!! Point taken. $\endgroup$ – Namaste Apr 25 '11 at 9:46
  • $\begingroup$ @Amy, @user9325: thanks. I don't want to close questions just because they're homework (or stated like homework) I think they're all valuable here, but imperative or homemwork or weird wording like 'Sir', they're still annoying (in different ways), and I thought a discussion would help me (us?) figure out how to respond appropriately. $\endgroup$ – Mitch Apr 25 '11 at 15:07

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