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I think that it would be a good idea to add another reason for closing a question, namely that the question is too basic, in the sense that the answer can easily be found through an Internet search and it is available at, say, Wikipedia, or Wolfram MathWorld. To be clear:

  • This is not meant to avoid closing questions for being duplicates. That is, if an Internet search shows that an answer already exists here, then the question should be closed as a duplicate.
  • It seems to me that the off-topic reason for closing question is used for many different things, and that's also why I am suggesting this.
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    $\begingroup$ The issue you describe is not that the question is too basic but rather that due diligence was not applied. How is this not covered by the 'lack of context' closing reason? $\endgroup$ – Andrés E. Caicedo Feb 6 at 13:57
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    $\begingroup$ (In particular, a 'too basic' closing reason seems against the spirit of the site, which is about questions 'at all levels'.) $\endgroup$ – Andrés E. Caicedo Feb 6 at 13:58
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    $\begingroup$ Basic questions are often only a step away from much deeper issues such as foundations of mathematics. This can make them surprisingly challenging to answer, but can also lead to very informative answers if done well. I think people often get frustrated with them because they don't know how to address the underlying issues in simple terms. $\endgroup$ – timtfj Feb 6 at 15:25
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    $\begingroup$ So I'm not sure there really is such a thing as a basic question in the end. How many pages did it take Russell and Whitehead to prove $2+2=4$? $\endgroup$ – timtfj Feb 6 at 15:31
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    $\begingroup$ My reference to “too basic” had nothing to do with the level of the question. I am thinking about questions such has: “I am familiar with the rational root theorem and I know how to use it. But I have no idea about why it holds. How can we prove it?” Such a question lacks no context and it is neither too elementary nor too advanced. But there are lots of places on the Internet where you can find proofs of this theorem. Thies is what I had in mind. $\endgroup$ – José Carlos Santos Feb 6 at 15:32
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    $\begingroup$ And it is important to you that if information is easily accessible elsewhere, then it shouldn't be accessible here? Can you explain why? $\endgroup$ – Najib Idrissi Feb 6 at 15:59
  • $\begingroup$ If someone posts a question here asking for the definition of field, that question will probably be closed (as off-topic), even if that person provides enough context. I just thought that things would be more clear for that person if the question was closed as too basic. And, no, I don't think that information easily accessible elsewhere shouldn't be accessible here. All I want is this: if we decide to close a question because it is too basic (in the sense that I described), then the person who asked it will better why the question was closed. $\endgroup$ – José Carlos Santos Feb 6 at 16:43
  • $\begingroup$ "If someone posts a question here asking for the definition of field, that question will probably be closed" I don't see why. $\endgroup$ – Najib Idrissi Feb 6 at 16:53
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    $\begingroup$ Why downvoting such a question ? For me it's a typical lack of tolerance one finds so often on the Internet. All sensible opinions have the right to be expressed, and arguing about them is good. I think that a criteria @José Carlos Santos has given "a question you can have the answer just by googling (in the case query formulation is easy)" is a really good separation line. $\endgroup$ – Jean Marie Feb 7 at 7:58
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    $\begingroup$ "Why downvoting such a question ?" -- Typically on Meta, for questions/suggestions of this type, upvoting/downvoting is less a statement of "this is a bad question," so much as a statement of agreement or disagreement. $\endgroup$ – Eevee Trainer Feb 7 at 9:28
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    $\begingroup$ @JeanMarie I just want to confirm what Eevee Trainer wrote: here on Meta, downvoting a suggestion means, in the first place, rejecting it. It should not be seen as an attack. $\endgroup$ – José Carlos Santos Feb 7 at 10:57
  • $\begingroup$ OK I will know for next time... $\endgroup$ – Jean Marie Feb 7 at 11:05
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Frankly for the type of question that you describe, two things are very likely:

  1. It is a duplicate
  2. It lacks context

On the off chance that both do not apply, I think it should not be closed per se. Maybe this particular piece of information is not so easy to find if certain keywords are omitted or not known. In such cases arguably the question adds value to the body of searchable mathematical information on the internet, and thus is a good fit to MSE.

A related question would be if we actually want MSE to be a place to ask about definitions to begin with. I think this is reasonable in general, and moreover I don't have the feeling that there is a problem with the amount of questions that do not fall under 1. or 2.

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I am strongly against the idea of closing questions as "too basic", if it is in the sense that the question is an elementary result in the field, or in the sense that the question has a simple solution. This is for two reasons:

  1. Who's to decide what's "too basic"? Among those $\geq3k$ users who can vote to close, there are professors of mathematics and physics, and I bet also some undergraduate or maybe even high school students. What's trivial for the former might not be so for the latter, so whether a question gets closed depends strongly on who's reviewing it, adding a strong air of subjectivity which I do not think is appropriate.
  2. We are not MathOverflow, where only professional mathematicians dwell. There are people from all levels of mathematics that can benefit from the site. If we were to require that questions not be "too basic", many otherwise valuable questions will be lost. Even if these questions aren't valuable to you, they may be to others.

However, I can see why you might want to close it if the question is not "too basic" in the above sense, but rather the "one Google search away from the answer" sense. In this case, I don't think the problem with the question would be that it's "too basic" per se, but that the questioner hasn't shown any research effort. But we already have a mechanism to deal with this: close as lack of context! Furthermore, it's quite possible that a beginner has a question about a concept but doesn't know the proper terms, so all of his attempts at googling turn out empty. In this case, even if the question is basic, it doesn't lack context, and I honestly think that it will be a good question for the site. Not only will a good answer help the questioner, but also future visitors.

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  • $\begingroup$ That is what lack of context is used for, but that is not at all what the words mean. English SE doesn't mince words and has a close reason for lack of research effort. $\endgroup$ – Matt Samuel Feb 10 at 0:58

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