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Sorry, this was most probably asked before in some form, but I haven't managed to find the original.

Let me describe a hypothetical situation related to this question. User $A$ posts a simple homework problem. Another user $B$ with quite respectable reputation (say $>5000$) gives an upvoted, though wrong answer, or correct answer obtained by wrong reasoning. After an exchange of comments, and finally an explicit request for $B$ to delete or correct his answer, nothing happens. Except that $B$ deletes his most glorious comments on the matter.

What should be done? Giving a correct answer doesn't seem to be an option, since most likely the only person who will read an already answered elementary question will be $A$. Should one flag the question or simply let it go down so that $B$ becomes even more respectable or...?

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Giving a correct answer doesn't seem to be an option...

It certainly is an option.

since most likely the only person who will read an already answered elementary question will be A.

You must be reading the already answered elementary question in order to be experiencing this conundrum, right? Moreover leaving a new answer will bump the question, which will almost certainly give it more views.

I think it is an excellent idea to leave your own answer when a question has an accepted answer that, after some careful thought and possibly dialogue with the accepted answerer, you believe to be incorrect. I encourage you to do so.

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Well, you can downvote any answer. You should do it if the answer is wrong.

Do not, however, flag the answer. It will be declined with the template

flags should not be used to indicate technical inaccuracies, or an altogether wrong answer

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There is no way to force another user to delete their answer. There are only three things you can do:

  • Politely point out the error in a comment

  • Downvote the answer

  • Leave your own, correct answer

These do not always leave a satisfying result, but there is nothing else that can be done within the structure that the website provides.

This sort of situation is one reason it is important to read answers carefully before voting, even if the person who wrote the answer has a high reputation.

At the same time, it is important to remember that, as an abstract principle, "correctness" of a natural-language proof can be interpreted differently by different readers. One person may think that a proof is just fine, while another thinks it has an enormous gap or begs the question. In most cases these disagreements can be worked out in comments, but not always.

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    $\begingroup$ Perhaps one should mention that the 20K+ "trusted users" have the ability to vote to delete answers with a negative score. $\endgroup$ – user642796 May 2 '13 at 13:35
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    $\begingroup$ @ArthurFischer: I would, however, not argue in favour of doing that to delete "wrong" answers. If the answer already has a negative score and has comments indicating that the answer is wrong, it may be more instructive to readers to leave the answer up instead of deleting it. $\endgroup$ – Willie Wong May 2 '13 at 13:50
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I think another possibility is just to edit the answer provided so that it is correct. I'm new to the community so I'm not certain about the etiquette of edits, but it seems like this is a good example of why the option exists. I have edited a couple answers already to have them be more clear or correct (in the case of an actual inaccuracy).

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    $\begingroup$ If the original author of the answer disagrees about whether it is correct, editing the answer against their wishes would be impolite. This has happened in the past; see meta.math.stackexchange.com/questions/793/… $\endgroup$ – Carl Mummert May 2 '13 at 13:40
  • $\begingroup$ Thanks for the link. Good to know that my edits have been accepted and meet the conditions for good editing presented in that question. I suppose if a question contains a serious content error there is not much else to do other than down vote. $\endgroup$ – agktmte May 2 '13 at 13:52
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    $\begingroup$ @agktmte. ... and leave a comment indicating why the answer is wrong. (When doing so, it is not at all necessary to say that you downvoted; this bit of information is of no actual use to anyone). $\endgroup$ – 75064 May 2 '13 at 14:01

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