Is sometimes keeping wrong answer reasonable?

Question

My memory might be fooling me, but I believe I have seen comments or discussions an meta regarding this matter. I am unable to find it now, so I will ask about your opinion.

If I answer some question and then it shows up that this answer is incorrect, are there sometimes reasons for not deleting an answer?

I can personally think of some situations like this:

1. This would help other answerers to avoid the same trap. (E.g., if there is one very "obvious" way to solve the problem, which is for some "not so obvious" reason wrong. Such situation could be a reason why similar incorrect answer will pop-up several times, after the preceding one is deleted.)

2. There is some information in comments, which I consider interesting and it would get lost by deleting an answer.

3. The question was misunderstood, so it is answer to a different question. But since I invested time into writing the answer and I find the information I've given in it interesting, I am not too keen do delete the answer.

I did not list partial answers here, since I believe they are ok. (At least for questions which, in their formulation, have several more-or-less independent part. Or for difficult questions, where we are only able to give partial answers.)

So are the above reasons sufficient to keep the answer? If not, how could the situation in cases like 1,2,3 be resolved?

Answer 1

Whether you delete any (deletable answer set within the constraints of the software) answer (incorrect or otherwise) should be up to you. But I would recommend that, if you know your answer to be incorrect (from discussions in the comments or other reasons) and choose not to delete it, please prominently state so at the top of the answer so other users don't have to wade into the comments to find out that there is a flaw in the argument.

Personally I delete all my wrong answers (and would copy the useful comments to a new comment on the question with proper attribution [mentioning that they were comments to my deleted wrong answer given by so-and-so]), except for when the question itself is ambiguous and open to interpretations.

Answer 2

1. Letting people start to read a wrong answer strengthens the wrong associations, even with a fat disclaimer this can have a negative effect. It is much better to think about at which point in the correct answer the "trap" is avoided and stress that point or ask in a comment that it be stressed.

2. Think about what the valuable content is exactly. The fact that you learned something from a reaction to your wrong solution does not make it an effective way to communicate this information to other people. Almost always the post would still better be deleted. In exceptional cases rewrite your answer to the effect that it says something like "In a previous version of this post I wrongly assumed that the integral converges, but I let it stand because of the marvelous heuristic for convergence given by X in the comment below." It would still be much better to just post a new question on heuristics for convergence and ask X to post their comment as answer there.

3. It is very unlikely that this is a legitimate reason because people tend to value their own time and investment so much that they overestimate the usefulness of an answer to "another question" and obviously do not care a lot of the misleading nature because they know what question they were answering. In the exceptional case that you proved something different much more elegant and interesting than the original question, there is no reason not to post a new question and put your own answer there for future reference.

Despite all this, there is no obligation whatsoever to delete a wrong answer, but you should not be surprised about downvotes, either.