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Should we answer questions like What is the difference between field and group in algebra ? I mean, how can someone serious about learning ask this here instead of looking it up in a textbook or in wikipedia?

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  • $\begingroup$ I'm at a bit of a loss of under what grounds to close it, given the options. "Too localized"? $\endgroup$ – Arturo Magidin Feb 24 '11 at 3:34
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    $\begingroup$ @Arturo: How about "not a real question"? Or can we create a new reason, say "waste of time" or "you must be joking"? :-) $\endgroup$ – lhf Feb 24 '11 at 3:39
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    $\begingroup$ I recommend downvoting and leaving it alone. You don't have to answer it, but there is no reason to forbid others to answer. There are lots of "let me google this for you" type questions on this site. I almost always downvote them if I see them. $\endgroup$ – Alex B. Feb 24 '11 at 3:42
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    $\begingroup$ See also: blog.stackoverflow.com/2011/02/are-some-questions-too-simple $\endgroup$ – Isaac Feb 24 '11 at 4:14
  • $\begingroup$ @Issac: that's exactly what I'm talking about. $\endgroup$ – lhf Feb 24 '11 at 9:38
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I think this type of question is too broad. The asker should specify what part of the definitions he didn't understand. And if it was not about definitions, he should explain what was the purpose of the question.

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I don't see why such a question shouldn't be allowed.

In fact I think it's a completely reasonable question, and one can imagine that the person asking is looking not just for a literal description of the difference (which they can presumably see for themselves by looking at the axioms of each structure and noting that they are different), but some cultural explanation of the differences, e.g. an explanation of what the two concepts are trying to model.

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    $\begingroup$ given how spare the question actually is, I think your answer reveals more about your fundamentally kind and generous nature than anything about the motivations of the questioner. But that's fine...I have no problem with the optimistic approach. :) $\endgroup$ – Pete L. Clark Feb 24 '11 at 6:10
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    $\begingroup$ +1 Pete :) ${}$ $\endgroup$ – Mariano Suárez-Álvarez Feb 24 '11 at 7:13
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    $\begingroup$ I was going to answer, but I see Matt already did: I do not see what the problem is with a question like this. Of course it admits a trivial answer when taken at face value, but in my opinion there are somewhat deeper questions that deserve to be addressed here. Why do we study these structures at all, for example. Is there one that is preferable to another in some cases? Groups measure symmetries of objects. What additional information do we gain from having a field structure? Can any (Abelian) group be extended to a field? Are there other kinds of (algebraic) structures that people study? $\endgroup$ – Andrés E. Caicedo Feb 24 '11 at 20:16
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I believe questions of this kind should be answered with as much good faith as possible.

I am not alone as there has been at least two answers when I first read this tread.

It seems there are two different kind of value that an expert can bring to a Q&A user:

  • precise, very factual, hard to find knowledge, digested and technically sound explanations, essentially closing a question, allowing the asker to use the answer directly for an application.

  • broad, synthetic, first outline of context and what is at stake, giving a perspective to someone who risks to loose himself in technical details or is just too new to have a good grasp of methodology and classical references.

To try to be coherent with my opinion, I have added a third answer to the question that motivated this thread. And I am interested by your opinion.

If S.E. is all about giving answerers a good environment, the illusion to be able to transmit their hard-earned intuition or personal broad picture could be part of that environment and motivation. And the occasion of confronting his or her vision with those of other experts and practitioners is fun. I believe this is already what happened.

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    $\begingroup$ Thanks for your answer here and in that thread. I'm all for people being generous, especially with their knowledge, expertise, and personal take. But in the case of that thread and in several others, I still don't see any effort of the OP to make the question clearer. That user in particular just asked and never returned to the site. $\endgroup$ – lhf Apr 25 '11 at 22:17
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    $\begingroup$ @lhf Good answers may help far more people than just the OP. Besides other readers of the thread when it is active, they may also help future readers that discover the thread by searches - whether here or by offsite search engines. $\endgroup$ – Bill Dubuque Apr 25 '11 at 22:29

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