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I answered a question of the form “Is my proof correct?”. From the proof, which was indeed correct, it was clear that the OP knew what he/she was doing, and I think that the doubt arose only because the proof was suspiciously simple—in essence, pointing out that the product of two non-negative quantities is non-negative. My answer was also simple: “Yes, your proof is correct. It really is that simple!”

The answer has already attracted a vote for deletion. Since the question did not receive any other answer (none being necessary), deleting my answer would leave the question unanswered. If the voter for deletion believed that my answer was inadequate, then he should have posted his own answer which addressed these supposed inadequacies. But perhaps I am missing something. Could someone here please advise me on how my answer could be improved so as to obviate such negative voting?

Remark: The question had many and various stylistic defects, which could have been remedied by extensive editing. However, I did not touch on these issues, because they would have muddied the waters and were essentially irrelevant to the OP's question.

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    $\begingroup$ "Check my proof" questions are always tricky to handle. If I am answering them I try to say more than just "you're correct", for example give an alternative proof or some brief insight. If I have nothing to add then I either write it as a comment, or answer as a Community Wiki (so it doesn't look like I'm getting rep. for nothing). $\endgroup$ – user1729 Jun 5 at 11:00
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    $\begingroup$ I disagree with your "Remark": it would have potentially made your answer valid. If you found the question trivial, as you told Asaf, you shouldn't have answered it. If you thought it was worth answering, then you should have answered it fully, not trivially. Students' proofs are often graded on style/method, as well as "getting a correct answer." $\endgroup$ – amWhy Jun 5 at 13:35
  • $\begingroup$ @amWhy : “Yes” on its own would have been a valid answer. The proof was too trivial to excite me into making much effort in editing it. For the OP, it was not so trivial that he could be sure of its correctness, and he needed the reassurance of an answer, which I gave in full. $\endgroup$ – John Bentin Jun 5 at 13:58
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    $\begingroup$ There is an interesting asymmetry between yes and no. The former may alone be an adequate answer to a question. If the answer is no, then generally more explanation is required, to point out just where and how the matter in question is at fault, and (if feasible) how to correct it, in a form that the OP will be able to understand. $\endgroup$ – John Bentin Jun 5 at 15:42
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    $\begingroup$ I think @user1729 phrased it well; either improve the post, or post an affirmation as community wiki. $\endgroup$ – amWhy Jun 5 at 19:42
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    $\begingroup$ I disagree with the comments that you need to "earn" the right to answer by doing busy work. $\endgroup$ – Andrés E. Caicedo Jun 5 at 20:00
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    $\begingroup$ @amWhy: The question isn't “Why is this proposition true/false?” but “Is my proof correct?” in the context that the OP clearly understands the proof and has got it right. The correct proof is already there, and only the answer yes is appropriate. If the proof is mistaken, the answer no, while technically correct, would be meager and of limited value if not accompanied by appropriate explanation. $\endgroup$ – John Bentin Jun 5 at 20:31
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    $\begingroup$ I agree with the answers, @AndrésE.Caicedo $\endgroup$ – amWhy Jun 5 at 20:59
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    $\begingroup$ @JohnBentin re asymmetry "Is there an error?" The asymmetry is hardly in "yes" and "no." (Yes, it's a nit-pick. Still.) $\endgroup$ – quid Jun 5 at 21:48
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    $\begingroup$ @XanderHenderson : True, I enjoy having my point of view affirmed. But I am also open to being persuaded otherwise by cogent rational argument. While you, quid, and amWhy oppose me, it appears that the MSE community generally is divided on this matter. I do not think that you can comfortably square this circle by ruling that questions of the type “Is my proof correct?”, when the proof is indeed correct, must be answered as if they had read “I know that my proof is correct, but please give me some tips about improving its presentation”. $\endgroup$ – John Bentin Jun 6 at 16:14
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    $\begingroup$ @JohnBentin your last comment distorts the situation. What is required is that a claim that is made is substantiated. Answer-posts that are only an unsubstantiated claim are not accepted. You apparently clearly understand this in the other direction, and seem to think that a question "Is this correct?" Should not be answered just by "No." but somehow should be interpreted and answered as "Is this correct? And if it is not, please explain why and best how to correct it." This discrepancy is rather glaring. What if a poster believes it is incorrect and just seeks confirmation for that believe? $\endgroup$ – quid Jun 6 at 17:36
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    $\begingroup$ @quid : I agree that claims made in an answer should be substantiated. The case in dispute is where the OP posts a correct proof of a proposition and asks whether it is correct. One way to substantiate the answer yes would be to prove the proposition, using a copy of the OP's proof, and say “There—I have proved the proposition, and your proof matches mine, so your proof must be valid too”. To extend the claim in your answer, from the OP's perspective, the credibility of any affirmation that the OP's proof is correct depends unavoidably on the credibility of whoever makes the affirmation. $\endgroup$ – John Bentin Jun 6 at 18:46
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    $\begingroup$ On the last part. Indeed, and therefore there should not simply be an affirmation but also a justification for the claim. We also require this for other answers. Usually, we do not consider as sufficient, answer-posts without deduction. "Q: What is the determinant of the matrix ?" "A: 25" "What is the value of this integral?" "5/7" In those case at last that the answer being correct is evidence that the answerer knows what they are doing and info is added. Indeed, there are some that will insist that this is sufficient, but given a large enough group most any view will find some support. $\endgroup$ – quid Jun 6 at 19:08
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    $\begingroup$ An actual problem with these questions is often that they are not focused on any issue. Likely, one should encourage the users asking them to articulate what specifically worries them. Otherwise we do proofreading (no pun intended) rather than answering a question. Anyway, as I said, I do not object if the (perceived) correctness is asserted as a comment; if I am alerted to such answers I delete them, or more precisely convert them to a comment. Thus, if you persist in your approach please at least use a comment rather than an answer. $\endgroup$ – quid Jun 6 at 22:17
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    $\begingroup$ This comment could be combined with an invitation to user asking to articulate any particular concern (if any). Something like "This proof looks correct to me. Why did you worry it was not correct? Is there any particular step you are not sure about?" If those are provided those could serve as a basis for an answer. If the reply to the comment just is "nothing particular, I just wanted to be sure" one can move on. And finally if the concern is that the questions stays unanswered then one could tell the OP to turn their proof-verification into an self-answered Q&A. $\endgroup$ – quid Jun 6 at 22:21
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This comes up frequently, and the meta-question is basically a duplicate (see below), but this time let me try to pin down the problem with this type of answer.

If verifying the answer is just as hard as answering the question, the answer-post adds nothing.

Let me elaborate. Literally just yesterday, I came across an answer to a similar question that said also "Yes, this is correct." just like here. No problem for some, it seems.

However, in that other case the account that gave the answer was completely new.

Let us step back. What does that answer actually add? All we really know is that somebody decided to post "Yes, this is correct."

The value of it initially hinges purely on the credibility of the user-account that posted it. Somebody could just as well simply throw it out there hoping for some votes that then, somewhat ironically, validate the answer. I mean, one could even write a bot for this: If tagged and body contains "Is this correct?", post answer "Yes, this is correct. Good job, well done."

Granted, if it comes from an account that, like in this case, does have credibility, there is some value to it. The value is in the act of the answer-post being produced, not in the post itself.

However, systematically it is not at all a good idea to allow a format of answers whose value comes only by way of the account to which they are linked. This goes directly against the entire idea of the site that posts are evaluated based on content, etc.

What if meta OP decided to delete their account in the next few months (I hope not, but for the sake of argument)? We'd have an essentially anonymous answer that asserts that something is correct.

What value does this have for somebody that cannot evaluate the veracity of the claim, which crucially includes basically everyone that actually would ask the question?

An answer to such a question should add some actual information and knowledge to the thread. For some ideas what one could include see, e.g., my answer to

How to answer proof-verification questions?

If somebody cannot or does not wish to add such a more detailed answer, but wants to add a quick note they still can comment. Indeed, that leaves the question formally unanswered, but in my opinion that is actually preferable in this case, and I do convert such answers to comments with some frequency.

The same goes for most "yes/no" questions.

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That may very well depend on the context.

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    $\begingroup$ For proof verification I find that if you spot places where stylistic improvement can be made, or simplifications, or otherwise improvements to the proof, you should mention that. It will make the answer better, and it will make the proof better. On that note, I will also remind everyone that proof verification questions are a subject that we, as a community, need to deal with at some point, exactly because of its propensity to produce "Yes, it's fine" as an answer, and the difficulty in applying "duplicate logic" to these questions. $\endgroup$ – Asaf Karagila Jun 5 at 11:19
  • $\begingroup$ Mentioning stylistic improvement for the question would have opened a can of worms. From a stylistic perspective, the question needed rewriting. While I have done that for questions that seemed worthy of it, this question was too trivial to motivate me to such labour. $\endgroup$ – John Bentin Jun 5 at 11:36
  • $\begingroup$ I'm not saying you need to rewrite the proof. I haven't even looked at your actual question at hand. I'm saying in general. If someone says "Hey, is this proof okay?" and you find places where the proof can be simplified, that is something worth mentioning. $\endgroup$ – Asaf Karagila Jun 5 at 12:53
  • $\begingroup$ Agreed. But this proof could not have been simplified significantly. $\endgroup$ – John Bentin Jun 5 at 13:04
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I answered the question being discussed in this meta-question. The first paragraph of my answer is, I think, relevant here:

In general, if a question on Math SE may be answered with a simple yes-or-no, then the question is almost certainly off-topic. There seems to be a consensus in the community that these kinds of proof verification problems are not off-topic, hence a correct answer to this question cannot be a simple yes-or-no. As such, I must assume that the question is really more about the style of the presentation, not the actual technical details.

I believe that this articulates a reasonable policy:

  1. Questions with simple yes/no answers are off-topic.

  2. Simple yes/no answers are low quality answers, and might be reasonably deleted.

  3. The and tags automatically indicate that the correctness of the argument is only part of the question being asked—the style or format of the presentation is also relevant.

This seems to be consistent with the principles articulated by quid here and in here in this thread. We arrive at the endpoint (I think), but from different directions.

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  • $\begingroup$ In this case, the OP was unconcerned about the style of his presentation (although that left much to be desired). The question was whether the proof was correct, which it was. What he needed was reassurance on this matter, which I gave—in the form of a direct answer to his question “Is my proof correct?”, namely “yes”. $\endgroup$ – John Bentin Jun 6 at 8:58
  • $\begingroup$ In my experience, people are happy when presented with a well-edited version of their writing as a fait accompli. In contrast, an unsolicited critique of their solecisms does not go down well. The OP's question should ideally have been edited, which in principle I could have done, but I lacked the time, energy, and motivation to do so. In any case, editing the question does not achieve the goal of lengthening the answer. $\endgroup$ – John Bentin Jun 6 at 9:25
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    $\begingroup$ @JohnBentin As I wrote above: a question with a simple yes/no answer is almost certainly off-topic. If the original asker is happy with a yes/no answer, then their question is not appropriate for Math SE, and should be closed and deleted. I order to reach a place where the question is on-topic, it is necessary for me to assume that the asker wants more than a simple yes/no. Thus a discussion of style is an appropriate response. An alternative proof would also be appropriate. As simple yes/no seems inappropriate. $\endgroup$ – Xander Henderson Jun 6 at 13:00
  • $\begingroup$ Let me turn it around: if the proof were incorrect, do you believe that the answer "No, your proof is wrong" would be considered acceptable? $\endgroup$ – Xander Henderson Jun 6 at 13:00
  • $\begingroup$ No. I described this asymmetry above in the fifth comment to the original question. $\endgroup$ – John Bentin Jun 6 at 13:16
  • $\begingroup$ @JohnBentin And you got comments there which pointed out flaws in your reasoning. $\endgroup$ – Xander Henderson Jun 6 at 13:18
  • $\begingroup$ No. The opposing comment (#7) was irrelevant, as I explained in comment #9. This comment in turn received only a flat denial in comment #11. $\endgroup$ – John Bentin Jun 6 at 13:43
  • $\begingroup$ @JohnBentin I am not going to engage in the reproduction of that thread here. $\endgroup$ – Xander Henderson Jun 6 at 13:52

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