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Suppose I see an answer which is pretty old (let's say older than a few months)
I have noticed a mistake, and after alerting the writer by comments I have received some comments in return which indicate that my correction has been somewhat acknowledged.
To what degree should I pursue the correction of the answer? Should I badger the answerer through comments, or just let it be? Or should there some middle-ground solution between the point where I feel that I am harassing someone, to the point I feel I am leaving a mistake out in the open?
You could always leave a comment by the answer in case nothing else works. You could then alert people, perhaps, here in meta, and those who agree with your comment can vote it up. Eventually peer pressure will do the job or at the very least there is a highly upvoted comment next to an answer.
This sounds similar to the premise in http://mathoverflow.net/questions/31337/ . While the advice there is somewhat pertinent, there is one big difference; postings on MathOverflow are subject to the Creative Commons license, and so someone other than the author is allowed to edit the post, especially if the answer is community wiki.
If it is bothersome, and you know some appropriate MathOverflow regulars to ask about the specific post (especially those who know the poster), see if they think the mistake is worth more than commenting on it. You can also ask the opinions of the moderators, although it might be best to ask someone who knows (for a period of more than two years) the author of the answer so that their reaction can be gauged. On MathOverflow alone, I have had reactions to suggesting that an error exist (or a possible improvement being made) ranging from enthusiastic endorsement to energetic denial or misunderstanding. You probably want some collegial support for your case if the latter is a possibility. Also Will Jagy among others can likely provide an instructive anecdote or two if he is reading this.
Gerhard "Helping Is Not Always Rewarding" Paseman, 2011.10.31
(I just have to say that the question grp linked has the coolest number possible.)
Thanks for the advice so far, I will give it a day or two before continuing my pursue for corrections.
In my mind what is most important is that wrong information not propagate too far. Leaving a comment pointing out the necessary correction, I think, suffices towards this purpose.
Also, yes, the number is awesome.
Will: I assume the answer is here.
Maybe I am lacking in etiquette, but what is wrong with giving another answer to the question? Especially since Asaf has already made an effort to draw attention to an error and was only partially acknowledged. It seems to me that questions ought to have correct answers, and that they ought to be answers, not comments.
I think it would be bad form, possibly also bad etiquette, to repeat someone else's answer and change it just enough to correct an error, or even to mention just the error as a separate answer, even if you started the post saying you were going to do that. If the intent is to correct someone's post in a minor fashion, I think a comment is more appropriate. Answers should be answers to the question, or at least substantial attempts at an answer, and contribute something new from the other answers.
I assume Asaf's situation concerns a minor error, otherwise his actions and reported reactions would be different. A correction to a major error that involves much explanation or departure from the given answer may be more appropriate for its own answer box, but I suspect that is not the situation which concerns Asaf.
Gerhard "Ask Me About System Design" Paseman, 2011.11.02
To be fair the situation that the answer has two mistakes. Both mistakes are not severe, but no typos either. The answer itself is mainly a quotation of an outside source with an addition of a proof not present in the mentioned link.
I tend to agree with grp on this manner. This is not a situation in which there is a grave mistake, but rather a fairly common mistake (well, maybe not as common as those in that 200+ answers thread... :-))
I think I will leave another comment, requesting the answerer to correct the answer. In case this will be a futile effort I'll reconsider Todd's suggestion.
To continue on Gerhard's point and to bring in a slightly different point of view:
To me what seems appropriate depends a lot on how large the error is/how clearly it is corrected by the comment.
I am rather hesitant to do minor edits to my answers, and also sometimes I am somewhat surprised when an original author or somebody else does very minor edits to their answers (like correcting a typo or so); basically I find the edit is noise [sometimes it happened to me a question I am interested in reapears on the frontpage, an answer seems to be edited, I look to see what is the new information, I do not notice anything, I check the edit history, one insignificant letter was changed...how disapointing]. As such if somebody would point out a minor error in one of my answers (not just a typo), but say I invoke a result without asserting that a condition is fulfilled that is non-obvioulsy but easy enough to be seen to be fulfilled or something like this, or some computational error, I might well just recomment 'Thank you for pointing this out (here is how to fix this)' and might conisder this as sufficient. Of course, if there is an error of the form that is difficult or only confusingly fixable by a comment the situation is different. But I do not think that each and every error however small needs to be fixed in the answer.
Yet, I strongly agree with Theo that no wrong information should propagte, I only wanted to point out that in my opnion not each error even causes this and/or that a comment can be a sufficient counter-measure.
Added: I wrote this before Asaf's last comment. To leave a second comment seems a good idea to me. As described depending on the precise circumstances the OP might not even be aware that somebody sees a need for an edit.
I agree with Todd. If you have a relevant contribution with mathematical substance in mind, you should not feel inhibited. I think this can include mathematical corrections to other answers, if they are sufficiently severe, easy to make when careless, or of independent interest. (The previous sentence was not meant to be a comprehensive list.)
Also, I think there is an ocean of wiggle room between a) posting a correction with some context and b) copying someone's post with minor alterations. The latter is generally considered plagiarism, and does not seem to be what most participants in this thread had in mind.