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In a mathoverflow answer, one usually doesn't want to provide all the details of a proof, especially if the question is not really research level (but not trivial enough to be closed). I feel that a vague outline is more than enough and the person who asked the question should work out the details themselves, or if they are stuck, ask in a comment, but only after putting in some effort. What do you think?

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The answer to a question should be written with the target audience of the site in mind, that is trained mathematicians, yet not necessarily experts in the subfield. (For very specialized and technical question, one can raise the expected background knowledge.)

An answer should be directly comprehensible; it should be possible to at least get the main point by reading just what is written attentively (possibly following links to external resources).

Of course it is not necessary to spell out all routine details, especially not if for an initial understanding it suffices to take them on faith. But the point of the answer should be made clear. In doubt it is better to give rather too many than too few details. A back-and-forth in comments is not optimal; one should write with the idea that initial version will suffice (not with the idea that clarification can be asked for anyway).

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    $\begingroup$ This is a good point; it may help to think of addressing not just a single person in one's answer, but rather a general audience, broadcasting one's knowledge to the world in a maximally useful way. $\endgroup$ – Todd Trimble Jan 7 '16 at 12:36
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    $\begingroup$ I click on the user name to try to ascertain the user's background so that I can tailor my answer appropriately. If it is a new user who does not identify himself or herself, I generally do not answer the question. A couple of times when the question was a very good one but I could not determine who the OP is, I left a comment to email me it the OP wanted an answer from me. $\endgroup$ – Bill Johnson Jan 11 '16 at 19:21

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