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  • Prove that every subgroup of index $2$ is normal.
  • Evaluate this integral: $\displaystyle\int_0^1 x^2 \, dx.$

If a question like that is posted, one suspects that the poster copied it from a homework assignment without even understanding what the question says. I have the impression that that is why "context" is asked for.

However, suppose it says:

  • How can I prove that blah blah blah.

and "blah blah blah" is a proposition that is easily, routinely, and quickly seen to be mistaken. That sort of thing seems unlikely to be a stenographically transcribed homework problem. Should the need for "context" apply in the same way and to the same degree in such a case?

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    $\begingroup$ This is not clear why this can't be a HW. I often ask students simple T/F questions in HWs/tests to test their basic understanding. Indeed, I remember at least two textbooks (one on abstract algebra, one on real analysis) where each HW section always starts with several T/F questions. $\endgroup$ – user99914 Apr 11 '18 at 4:45
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    $\begingroup$ While I admire your optimism, people sometimes make mistakes when copying. $\endgroup$ – Najib Idrissi Apr 11 '18 at 5:43
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    $\begingroup$ Context is not just needed for homework questions. $\endgroup$ – Michael Greinecker Apr 11 '18 at 8:59
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    $\begingroup$ Upvotes in Meta mean we agree, downvotes mean we disagree. However, when a question has the form "Should the need for context apply in the same way..." it may be confusing which direction to vote. Do the downvoters mean that the need for context should not apply in the cases described? which would be agreement with what the OP argues in "However"... $\endgroup$ – GEdgar Apr 11 '18 at 13:21
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    $\begingroup$ @GEdgar generally voting is aligned with the intent of a post. $\endgroup$ – quid Apr 11 '18 at 14:20
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    $\begingroup$ @MichaelGreinecker : The big problem I have with this is that, aside from the case of demonstrating that you have a question in your mind instead of copying a question you don't understand, there is no clear definition of "context" nor any clear account of why it is needed. $\endgroup$ – Michael Hardy Apr 11 '18 at 14:58
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    $\begingroup$ @MichaelHardy You keep asking for definition of context. Several users mentioned in another discussion (including me) that How to ask a good question. - Provide Context details what context can (should) look like. (If that description seems not detailed enough, maybe this question could be revisited: What Do We Mean by “Context”?) $\endgroup$ – Martin Sleziak Apr 12 '18 at 4:20
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I have the impression that that is why "context" is asked for.

That is a misconception.

Should the need for "context" apply in the same way and to the same degree in such a case?

Context is even more important in the latter case. Look, you proved it yourself. You state what one can reasonably suspect in the first case. However, in the second case we are at a loss. "Why is two plus two equal to five?" Why would somebody ask this? Context is crucial to understand the question.

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  • $\begingroup$ As I said in another comment, the big problem I have with this is that, aside from the case of demonstrating that you have a question in your mind instead of copying a question you don't understand, there is no clear definition of "context" nor any clear account of why it is needed. $\endgroup$ – Michael Hardy Apr 11 '18 at 15:01
  • $\begingroup$ $\ldots\,$ and I don't see why I must be at a loss in such a case. Someone recently asked how to prove the cardinality of a certain set is $2^n.$ I posted an answer, showing that it's actually $2^{n-1}-1.$ Why would I be at a loss there? $\endgroup$ – Michael Hardy Apr 11 '18 at 15:03
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    $\begingroup$ 'there is no clear definition of "context"' there are various accounts of what counts as context 'nor any clear account of why it is needed' In a way that's actually tangential, but there are various accounts of that too. $\endgroup$ – quid Apr 11 '18 at 15:08
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    $\begingroup$ So why did OP ask to show it is $2^n$? Maybe they were talking about another set? Maybe there is another misconception to be addressed? Either way the situation, the context if you want, of the post is much less clear. Incidentally, others argue that for your first type of question no context is needed as it is clear anyway what is actually expected. I contest this too, but it makes relatively more sense to me then the proposition that a post that asks why something false is true does not benefit from further explanation and is best addressed by turning the statement into something true. $\endgroup$ – quid Apr 11 '18 at 15:13
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    $\begingroup$ Finally, even if some believe that providing the context is not crucial, it can hardly be very harmful. Thus, in case of conflicting opinions it seems clear that the one asking for context should prevail. Context that is presented can still be ignored, context that is not present cannot be taken into account. $\endgroup$ – quid Apr 11 '18 at 15:16
  • $\begingroup$ But the fact that something that could "hardly be harmful" is omitted, that is not a reason to close a question. $\endgroup$ – Michael Hardy Apr 11 '18 at 19:10
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    $\begingroup$ Please read again what I wrote. Here is an aid: "even if some believe that providing the context is not crucial" [some others think it is crucial] and "in case of conflicting opinions it seems clear that the one asking for context should prevail" [because some find it crucial while others can hardly find it harmful even if not crucial]. $\endgroup$ – quid Apr 11 '18 at 22:21
  • $\begingroup$ @quid I don't think that is a valid argument, since the immediate consequence is closing a question, which can be seen as harmful (for instance, if you value the website most as a repository of knowledge). In the eyes of someone who does not think context is crucial, what is happening is that a question is being closed for lack of something which is not crucial, so there is a net negative for the situation. $\endgroup$ – Aloizio Macedo Apr 12 '18 at 3:37
  • $\begingroup$ In essence what is being said is "Between those two situations (X,Y) which have net negatives in the respective points of view, X should be favored, because one 'arbitrary' reason among the things which contribute to the net value is positive for X and at least null for Y", and then you are disregarding the other things which contribute to such value. What should be argued (imho) is why the reason in question (i.e., context) is not arbitrary and deserves special consideration. $\endgroup$ – Aloizio Macedo Apr 12 '18 at 3:46
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    $\begingroup$ @AloizioMacedo I think it is a valid argument, but there are valid counter arguments :-) One of which you gave. But this discussion is a bit orthogonal to the specific concern; I do not intend to redo the entire context -debate here. (Maybe I should not have brought up that part to begin with). The question here is whether for questions that are false context is less needed than for questions that are correct. I don't think so, if anything the converse. $\endgroup$ – quid Apr 12 '18 at 8:31
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here is one from a few days ago

Equivalence of Equivalence Class of Binary Quadratic Forms and Ideals

If the kid had been truthful about any of it, it probably would have given some sort of usable answer. But he, very carefully, made an image of just the theorem from Cohen's book. If you look at the comments, he could not understand Cohen and demanded an easy proof.

I always want the source of a problem and the background of the student. Often they seem to be avoiding giving that precise information

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  • $\begingroup$ You always want the source of the problem and the background? I am surprised to hear that. I know of many questions that have received many up-votes and many highly up-voted answers and compliments from the more respected posters to m.s.e. where no such information was present. Will you claim that if I look at questions that you have answered at length, that information will always be there? (I haven't looked yet. I'm not sure whether I will.) $\endgroup$ – Michael Hardy Apr 11 '18 at 18:45
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    $\begingroup$ @MichaelHardy I always want that information. I don't always ask. It's likely that I rarely ask, as my attempts years ago in that direction bore little fruit $\endgroup$ – Will Jagy Apr 11 '18 at 18:54
  • $\begingroup$ ok, In the following question, is there something that you consider to be "context"? math.stackexchange.com/questions/2729677/… $\endgroup$ – Michael Hardy Apr 11 '18 at 19:08
  • $\begingroup$ @MichaelHardy not really. That user is a bit flighty, he asks all sorts of things. If it had not been a topic i knew well, enjoyed, and had already programmed, I would likely have ignored it. $\endgroup$ – Will Jagy Apr 11 '18 at 19:12
  • $\begingroup$ So you would have ignored it, but that's not the same as voting to close it, which is what people often do when they think there's a lack of context. $\endgroup$ – Michael Hardy Apr 11 '18 at 19:14

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