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Why do users give answers using alternative method when I'm asking what went wrong with my solution?
Many aspects to this. I agree to a great extent with the points raised in the other answers. Yes, there are XY problems. Yes, the question is not here just for the benefit of the asker, and this shows in our expectations and also in the answers.
I want to emphasize one aspect not present in the other answers.
The actual mathematical problem underlying ...
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1) A homework problem (with book citation)
Excellent. This provides part of the context, namely where the problem came from. Sadly, many other people don't even bother to state this, and is one possible factor for closure.
2) The inquirer's workings towards an (ultimately incorrect) final answer
Great. As long as it is readable, it is perfect.
3) The ...
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Most of the time it is in my opinion and observation possible to give a more detailed answer.
Points that can often be addressed include:
Suggesting minor improvements of the presentation or variations.
Giving a high-level summary of the argument.
Mentioning points where details might be added (even if not strictly needed).
Putting the argument in a ...
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Why do users give answers using alternative method when I'm asking what went wrong with my solution?
Not the exact answer to your situation, but it might give some idea, so in that sense, this answer is also an alternative answer to the question that you are asking.
We are not your tutor in here, nor this is a website you are getting personalised service; even though you are owner of your own question, the main purpose of that question is to both help you, ...
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I don't think it's a good idea to post your attempt at an answer. If you're not sure about it, then it is more a part of the question. If you figure it out after asking, though, go ahead and post your new solution.
I include my attempt in the question. I start by stating the problem, which I highlight with a > to make it stand out. Then I give my general ...
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Your first example is structured like this:
[mathematical statement]
Is this statement true or false and why?
[attempt at proof]
Is this way of looking at it right or not?
It is entirely fair to answer that question with a different proof. This OP doesn't know whether the statement is true or false. Proving it false is an answer to the question.
The ...
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As detailed elsewhere (see How to answer proof-verification questions?) I do not consider it as best practice to post only "this is correct" as an answer. Usually, something more can be said to make for an actual post (see the above mentioned post).
Dually, I agree with the view expressed on Best way of asking "check my proof" questions, that ...
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The main danger with asking multiple questions on a single theorem is that you could easily write several posts where the effort required from answerers is duplicated from question to question - for instance, if answerers must read significant chunks of identical text or point out the same error over and over.
This doesn't rule out asking about multiple ...
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It seems that there are two separate issues in what you are asking. So let me address them separately:
Is it okay if I use this site to have someone check my work?
This was discussed here on meta many times, you can check some questions tagged solution-verification here on meta. For example: http://meta.math.stackexchange.com/questions/4597/best-way-of-...
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The best way to ask check-my-proof questions is not to simply ask users to check your proof. In what follows I've been strongly influenced by Raphael's answer on meta.cs.SE, and somewhat echo Qiaochu Yuan's answer to a previous meta.math.SE question.
Questions of the form
I have to prove that if ${D_{M,K}}$ is a universal factor, then $\Psi \le-1$. Here'...
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When I first started studying rigorous mathematics I couldn't tell a proof from a carrot. I wasn't in a formal educational institution at the time and relied heavily on feedback from mentors in my personal life that were well trained in mathematics. If it weren't for them I would be at a very different place professionally today.
The reason I share this ...
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If you haven't yet received an answer, answer it yourself. That way, no one will add an answer which merely expresses what you'd already discovered yourself (which would be a waste of time) and your question can be taken off the unanswered list.
If you have received a (useful) answer, then maybe leave a comment on your question. If an answer helped you ...
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In my opinion, no, you do not need to say in the title that it is a proof-verification --- in fact, you do not even need to say that it is a proof.
Phrases such as
"Prove that", "Proving that", "How to prove", "Solve", "How to solve", "How to show", etc. in titles usually don't add any meaning to a question. That is to say,
These phrases should be used in ...
8
It really depends on where you are in learning mathematics. If you're at the stage where you can look at a proof and be confident about whether it is correct, then asking such questions is not likely to have great value to you (and you'll probably recognize that) - the challenge of mathematics would be more in generating the proofs than in checking them. ...
7
The -verification questions are either the the worst ("too localized") or the best (maximum "research effort") type of question on the site. Opinions differ.
The important thing is to add the tag proof-verification or solution-verification so as to advertise the nature of the question clearly, and machine-readably. Without the tag, there is no way to see ...
7
Ask for proof verification and ask for other ways to prove the same statement. One or two questions?
I would advice you to put it in one question. You should tag it as proof-verfication and as alternative-proof, along with other tags regarding the field of the question.
If you will have two questions, then the question about another proof will have to show some attempts. If you post the same proof again, then people will do double work, namely then they ...
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(Too long for a comment, but this is not really an answer).
You're right - these are not typically good "archival" questions. Later users benefit somewhat less from stumbling across these questions compared to a standard well-defined question+good answer.
But many users here view MSE as a teaching platform, and worry a bit less about the later user and ...
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Two aims are involved here: (1) we need discipline on the site to keep answers relevant to the questions to which they are attached; (2) we do not want to make people feel bad about posting a correct and elegant proof of a result for the enlightenment of those who, whether as OP or visitor, have evinced some interest in the result.
We would be entirely ...
7
What is the usefulness of having "proof-verification" and "solution-verification" as different tags?
While there could be some meaningful distinction (in theory) this does not seem to work well in practice. I checked a bit manually, and also observed that 150 questions (this are almost 20 percent) of the questions tagged solution-verfication contain the word "prove" (and rather not in the way "I do not need to prove this I just need the solution").
To ...
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Yes, as long as you show your work and make sure the question hasn't been asked before!
That is, surf the "set-theory" tag a while, and maybe you'll find answers to your questions. Also, exploit the search button.
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It's a good question, and one I have no universal response to.
I dislike the flat "Yes, that's correct" response though I have used it.
It's effectively meaningless. At best it is Proof by Authority. At worst? Well, many users here are heavily credentialed but it's all anonymous. I have seen many instances in which people confirmed entirely ...
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No problem whatsoever. Remember to show your work, give context and details. That's all.
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What to do when someone ask for a mistake, comment indicating where he made the mistake or answer indicating where he made the mistake?
If what they seek is the mistake, and you wish to state what that mistake is, I would post that as an answer - preferably with an analysis of why this is a mistake, and perhaps a hint or nudge at how to correct it if the ...
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I would say that such a question is not a duplicate, so it should not be closed as such (after all, different questions about the same problem need not be duplicates).
However, once the OP has had sufficient feedback on the attempted proof, I think the best course of action would be:
First, the OP posts the full proof as an answer, in order to get final ...
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Why do users give answers using alternative method when I'm asking what went wrong with my solution?
I think you made your question clear enough in the initial posting, and I think everyone contributing to the discussion here would have endeavoured to answer the question you asked, not solved the problem you were working on (as well they should).
As I said, I don't think this is the case for this particular question, but sometimes answering questions like ...
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