Ironically, I'll bet this question is a duplicate of other questions regarding duplicates, but I see little harm in sparking some new conversation here, even if we tread over old ground that many others may not have seen.

In any case, the question I want to pose is this: When is a duplicate really a duplicate? I ask this because I answered this question in some considerable detail, only to see it marked as a duplicate of this question. Upon inspection of the duplicate charge, I saw that the so-called duplicate question was not so: the integrals discussed in each question were related tangentially by an integration by parts. (Actually, the original alleged duplicate question involved a sum and not an integral, but never mind.)

Luckily for me, I happen to hold gold badges in the tags of the question I answered, so that I was able to exercise the power to unilaterally reopen the question. But that is neither here nor there. What I want to know is, what on earth is a duplicate?

Is it a question that asks a duplicate, i.e., exactly the same question as another?

Is it a question that may not be a true duplicate of another question, but produces the same answers?

Is it a question that that may not even generate the same answers, but poses essentially the same challenge?

Or is it something else?

I'd like to hear from others, because I am under the impression that a duplicate is an exact copy, and those who answer such questions may be asked to migrate their answers, if unique, to the original question. (I have done this in the past. I will not do this in the case cited here because it would be ridiculous.)

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    $\begingroup$ Ideally, I'd say that two questions are duplicate if you can take any answer for the old question and post it verbatim as an answer for the new question (maybe with a few changes in notation). In practice I think it's also common (and desirable) to close as duplicate when one or two trivial steps are necessary to go from one question to the other -- for a stupid example, one question might ask about rings whose all prime ideals are maximal while the other asks about rings of Krull dimension zero... That's not the case here: going from one to the other is not a trivial computation. $\endgroup$ – Najib Idrissi Dec 26 '14 at 15:04
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    $\begingroup$ For some perspective, the FAQ says one should vote to close questions as duplicates when "they are sufficiently similar to existing questions and would be answered identically to them." Something else to consider: unregistered users get automatically redirected when they look up a question that was closed as a duplicate. I doubt someone looking up how to compute $\int x \cos x / (1 \sin^2 x) dx$ would be happy to get redirected to the computation of this sum. $\endgroup$ – Najib Idrissi Dec 26 '14 at 15:07
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    $\begingroup$ @NajibIdrissi: Thanks, I appreciate the input, even if I disagree strongly. I think that, in a site like this with an extremely high volume of questions, it would take the community way too much effort to draw a necessarily subjective line between duplicate/not. In the case I outlined, the expressions of the questions were vastly different and motivated different approaches. I am of the opinion that duplicate should be a real duplicate, and leave it at that. $\endgroup$ – Ron Gordon Dec 26 '14 at 15:09
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    $\begingroup$ No, there definitely should be some amount of wiggle... Suppose someone asks how to compute $\sum_{k={\color{red} 0}}^n k^3$ and then someone asks how to compute $\sum_{k={\color{red} 1}}^n k^3$... Wouldn't you be tempted to close as a duplicate? But it's not the exact same question. In this particular case the questions are unrelated enough that closing is not warranted. But it can happen that a trivial, obvious step can make an answer to question A also an answer to question B. When this happens, I'm in favor of closing. $\endgroup$ – Najib Idrissi Dec 26 '14 at 15:13
  • $\begingroup$ (BTW, maybe you didn't notice, but I was the one who complained first in the comments of the question you linked that I didn't believe it was a duplicate... I'm not disagreeing with you about this particular case, I'm saying that it can happen sometimes) $\endgroup$ – Najib Idrissi Dec 26 '14 at 15:19
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    $\begingroup$ @NajibIdrissi: Not to be extreme, but I'm not so sure. It depends on the answers generated, IMO. Anyway, at what point do you not mark as a duplicate? Because in the case I showed, I disagreed strongly because...how many other questions on the site could be marked as duplicates under that criteria? $\endgroup$ – Ron Gordon Dec 26 '14 at 15:20
  • $\begingroup$ @NajibIdrissi: I didn't notice, and I appreciate that you agree with me there. $\endgroup$ – Ron Gordon Dec 26 '14 at 15:21
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    $\begingroup$ If I can envision my explanation to why answer to question A also answers question B taking more than a single line, or requiring the use of the word theorem/lemma/... (as in "by ...'s theorem", "by the ... lemma") or some other advanced notion, I don't vote to close as a duplicate. I think it's a reasonable criterion. Though I agree it's very subjective, and I'm not sure I apply that consistently. $\endgroup$ – Najib Idrissi Dec 26 '14 at 15:26
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    $\begingroup$ For my two cents, I agree with @Najib. I also think that the "abstract duplicates initiative" should be continued as a means to point to the broader picture. Closing after some period of time could be seen as a kind of third option in my opinion, to enhance the value of MSE as a knowledge repository. $\endgroup$ – Lord_Farin Dec 26 '14 at 17:12
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    $\begingroup$ If I can easily envision a student having trouble making the connection, I don’t consider it a duplicate. For a fair number of students @Najib’s questions are, sadly, not duplicates, for the reason that Thomas gives in his answer. $\endgroup$ – Brian M. Scott Dec 28 '14 at 8:02
  • $\begingroup$ @BrianM.Scott I don't expect the students to make the connection themselves; the length requirement is there so that a short comment is enough to explain the connection. $\endgroup$ – Najib Idrissi Dec 28 '14 at 10:45
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    $\begingroup$ Even thought the equivalence of these two particular questions is not immediately obvious, the necessary steps to connect the two are explained at the beginning of the accepted answer to the first one (in fact the method of solution there is to go back from the sum to the original integral), so that answer also contains an answer to the second question. In my opinion, this ought to be enough to consider the questions as duplicates, but apparently some people feel strongly different, and I'm not going to enter into a fight about this. $\endgroup$ – Hans Lundmark Jan 3 '15 at 20:28
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    $\begingroup$ There is a new discussion on meta with rather similar focus: How close a match we need to close a recurring question as a duplicate? $\endgroup$ – Martin Sleziak Jun 18 '16 at 4:02
  • $\begingroup$ Thanks @MartinSleziak. $\endgroup$ – Ron Gordon Jun 18 '16 at 8:55

The following might best be viewed as a long comment.

First: There will always be cases where five or more people will decide on the wrong thing to do.

Second: I think it is hard to give a clear cut algorithm for deciding if a given question is a duplicate of another.

But here are some thoughts:

  1. My opinion is to only close questions that are asking the the "same" question. I think it should always be about the question and never about the answer. Therefore, two questions are not duplicates even if they can be answered with the same answer. Lots of very different questions have the same answer yes.

  2. I disagree with closing a question because it is an abstract duplicate. It might be very clear to you and me that the questions basically ask the same, but to a student of the subject this might not be clear at all. Many questions can be answered as being applications of theorems. But the problem is that applying a theorem isn't always easy. Likewise, one might know how to find $$ \sum_{i=1}^n i^3 $$ because this is "just a formula" to be memorized. But asking about $$ \sum_{i=2}^n i^3 $$ is harder because more work is required than just memorizing a formula. Therefore I would view these two sums as two distinct questions. And I think a good answer is to link to the other question and then provide the remaining parts (or hints). But, as mentioned about, it is hard, because if we compare the sum with starting at $i=1$ to the one starting at $i=0$, then I might fall on the side of saying that they are duplicates. We have to remember that a person going through a subject for the first time doesn't view the problem the way an experienced person does.

    I disagree with the notion that "Once you know how to solve one of these problems you can solve them all.". My students can often solve one problem, but a very similar problem they had absolutely no idea about. Yes, as a teacher it takes quite some time before you realize this! To me the two problems are nearly identical, but to the student, they look completely different. One thing that I try to teach my students is exactly the idea that the same strategy works on many problems. But this takes time to realize and master.

    When I have asked questions elsewhere, I have often been frustrated that my question was closed (and then deleted) because it had an abstract duplicate. I would go to the duplicate question and read the answers, but I didn't see the connection. This has, though, forced me to be more careful when I ask questions. I now try harder to be more precise about what exactly my question is. I do more research before asking and if possible I make references to the questions that are close to mine and then I explain why I still don't get it.

  3. We allow: please-check-my-work problems. Therefore I guess we would consider two questions different even if they are about exactly the same thing if different work is showed. Two people might have the same problem but struggle with different aspects of the solution. Therefore in essence the questions are different.

In this way I think some of this is related to the discussion about the questions that don't show any effort (the so-called PSQs).

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    $\begingroup$ I do agree with a lot, and would agree with even more if the notion of "answer" was more constrained on this site. It strikes me as somewhat incompatible to apply very fine distinctions when deciding when questions are different, and to allow, and even encourage, at the same time, the often somewhat generic "Hint" as answer. $\endgroup$ – quid Dec 27 '14 at 19:46
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    $\begingroup$ I agree with you on all three points. I am especially annoyed when requests for commentary on the OP’s proof or calculation are treated as duplicates of requests for a proof or calculation (or hints for same). $\endgroup$ – Brian M. Scott Dec 28 '14 at 4:39
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    $\begingroup$ @Brian I strongly agree. I've proceeded to start awarding such answers displaying a lack of interest in helping OP in favour of internet points with downvotes, always accompanied by a comment explaining the situation. $\endgroup$ – Lord_Farin Dec 28 '14 at 9:45
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    $\begingroup$ In addition, I think that 2 and 3 are excellent candidates for delayed closure - say, after an answer has been accepted, or several days/weeks have gone by. $\endgroup$ – Lord_Farin Dec 28 '14 at 12:10
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    $\begingroup$ Sorry to belabor the point but please see math.stackexchange.com/a/1084028 and math.stackexchange.com/a/1083966 to see what I mean. Note these are answers to different questions, by the same OP, asked within an hour or so. $\endgroup$ – quid Dec 29 '14 at 0:11

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