Questions that specify an approach

Question

There are instances where a question is asked with a specification on how the user wants to approach a problem, but the answers don't follow that instruction. This question is a good example. I gave an answer, so this may be self-indulgent, but although the OP stated in the question that they needed help with induction, some answers never touched on induction. I did like those other answers, but if the question is "How do I prove this with induction?" I don't think that they can be considered answers to that question. How should questions like these be treated? Is it bad form to answer a question differently from how the OP requests?

As argued before on this question, it doesn't detract to provide an alternate approach to a proof, and I agree that it's nice to see those other answers. However, I still think that those answers are answering a slightly different question, and not the question given. On that same thread, users argued that the questioner is owed nothing and should be grateful to any answer, but I think that there is value to questions with specific restrictions.

I think that part of the problem is that users asking this question often do so because they need help with homework/classes and they'll disregard more advanced/elegant proofs for ones they can write on their homework/understand. People get annoyed if they're asked to prove something more elementarily to help that one user, and that's fair. Plus, the answer will still be of use to users who have the necessary background. Regardless of the intent of the OP, though, I'd argue that these types of questions are still valid, because it's useful to see an elementary proof or just see a different method. Can a question like "How to prove this using x?" be treated as just "How to prove this?"?

Answer 1

The specific case you link to seems very clear cut. I agree that some of the answers are not good answers to the question asked (or even answers at all). OP was specifically seeking an inductive argument to understand (strong) induction; the specific problem was not all that relevant. To give an altogether different argument for the problem at hand seems besides the point. A relatively better answer would have been to provide an argument using (strong) induction for some other problem.

And also generally I think that "How to prove this using x?" should not be treated as just "How to prove this?"

However, for what this means in practice there is a range of possibilities and it will depend on context. Yet, I think basically always the presence of the request should be acknowledge in some way.

There are already some answers using X as requested. I'll still add a neat argument using Y: ...

I think this can be a meaningful addition. Sometimes it might not, but in any case it should be harmless. A relevant point is that the questions with X was already answered. However, even an answer like this can be fine:

I do not know how to do this using X as requested. But here is an argument using Y: ...

I'd say such an answer can be relevant after some time has passed without another answer, especially in cases where the "using X" might not be central requirement but rather OP's idea or preference.

Another thing that can happen could be.

I do not believe one can do this in a reasonable way just using X because {some argument}. But here is an argument using Y: ...

To me a key point is that one should at least make clear how specifically the answer relates to the questions as asked. Different people can come to different judgments what could be useful as answer, and that's fine. But I have a strong preference that such a decision is somehow documented (as it avoid confusion and arguments) and a conscious act.

The practice not to even parse the full post before posting what one believes ought to answer the question is a malpractice.

Of course everybody can overlook some condition imposed sometimes, it certainly happened to me. However, there are some users that basically verbatim say they only read the title of a question and find nothing wrong with this. I find this unacceptable, though there is unfortunately not that much to be done against it.

Answer 2

It's perfectly reasonable for the OP to ask for a solution or proof that doesn't involve advanced methods which would go beyond the OP's present state of education, and that request should be respected. However, it can happen that the OP demands a (complicated) proof in a certain style when a more elementary and altogether better proof is available. In that case, pandering to the OP by supplying a proof of the demanded type is teaching bad mathematics. Any proof is better than none. But, if we have a simple and elementary proof, there is no virtue in replacing it by a laborious and convoluted one.