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Since I self-study mathematical analysis without formal teacher, I can only appeal to help from out site most of the time. It's obvious that to grasp the underlying concepts in mathematics, we must roll the sleeves and solve problems.

It's clear that there are actually mistakes and misunderstanding that are too subtle for me to recognize, so it's very natural for me to ask for proof verifications.

Even though I tried to write my proofs as detailed and clear as possible, they seem to attract little attention from other users. It seems to me that proof checking is a boring and tedious job, but it is essential for me (and possibly for all of us) to know whether and where I get wrong.

How can I make my post for proof verification more attractive and consequently attract more attention?

Below are questions that i have not received any answer. Most of them are related to Cantor-Bernstein-Schröder theorem. It would be great if someone can help me improve them so that they get an answer. Thank you so much!

Is this a mistake in the proof of Hall's Marriage Theorem from https://proofwiki.org?

Top-down and Bottom-up proofs of a lemma used to prove Cantor-Bernstein-Schröder theorem and their connection (this is the question that i would like to receive answer most)

Is my proof of Cantor-Bernstein-Schröder theorem correct?

Bottom-up proof of a lemma used to prove Bernstein-Schröder theorem

Julius König's proof of Schröder–Bernstein theorem

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migrated from math.stackexchange.com Aug 11 '18 at 14:30

This question came from our site for people studying math at any level and professionals in related fields.

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    $\begingroup$ It would also help answering if you gave here a list of questions which, in your opinion, haven't received enough attention (that's possibly borderline regarding the rules of the site, but I'm asking - and you can delete them later if someone complains). You can add them in a comment to my answer, or here, if you don't want to bump your question. $\endgroup$ – Arnaud Mortier Aug 11 '18 at 11:58
  • $\begingroup$ @Le In light of the questions listed, I see that you are talking about complete proofs where you are not sure whether there is a gap or not. For this kind of proof the best advice I can give you is train your own eye, learn to question yourself, and break the proofs down to more pieces at places where they look suspicious. $\endgroup$ – Arnaud Mortier Aug 11 '18 at 12:26
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    $\begingroup$ I feel like you are able to articulate a proof(possibly not 100% correct/formal) of C-B-S you should be able to articulate some idea of what could be wrong, and it seems you do have a grasp on the logic you would need to check these proofs(and one of your questions is you checking someones proof, pointing out a specific detail you are unsure of). It sort of seems like you are looking fore a grader to nitpick your proof, which probably is not what most people who answer questions want to do, so that is probably one reason you are not getting answers. $\endgroup$ – Paul Plummer Aug 11 '18 at 20:11
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    $\begingroup$ I avoid "is my proof correct" questions for two reasons. I figure giving you these reasons may help you understand how to improve your questions. 1. to answer correctly and fully I would have to write out the result myself - reading a proof is insufficient (e.g. misreading, not spotting missed cases, etc.), and 2. I can never be fully confident with a "yes, it's correct" answer (because of reason 1., above), while a "no" answer is easy. So possibly, if you have no answers then you may be correct(-ish). $\endgroup$ – user1729 Aug 13 '18 at 9:59
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Sometimes how attractive a question is is also a matter of luck, of who is connected at the time you ask. But in general here are a few tips:

  • Avoid asking ten questions in one (I've seen that)
  • Try to emphasize the point - even if the context requires some terminology and perhaps an unavoidable long text, you can always give a clear and short introduction where people will see immediately if they can answer or not.
  • If it has to be long, try to be as structured as possible, using - bullet point lists, **bold** and *emphasized text*, ## Titles ##, > quotes etc.

  • Offer a bounty (if the question really needs efforts from the answerer).

  • Of course, explain why/where what you have tried has failed.

  • Explain briefly the points that you have understood (I've seen someone say that they had understood why the probability of something was 13, which was quite helpful in answering)

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  • $\begingroup$ I have added not-answered questions to my thread as you suggested. Thank you so much! $\endgroup$ – Le Anh Dung Aug 11 '18 at 12:15
  • $\begingroup$ I feel that this doesn't answer the question - it is too generic (in particular, "explain why/where what you have tried has failed" is irrelevant here). I would be interested to see a more focused answer to this question, as I genuinely have no idea what the answer should be (any always avoid "is my proof correct" questions). $\endgroup$ – user1729 Aug 13 '18 at 9:55
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    $\begingroup$ @user1729 at the time I answered there were no examples and the question could be interpreted in different ways - it was itself more generic. Now there is clearly more that can be said, you should add another answer if you have ideas! $\endgroup$ – Arnaud Mortier Aug 13 '18 at 12:57
  • $\begingroup$ @TiwaAina please ask before making edits. 13 is actually what I intended to write, that is the whole point. $\endgroup$ – Arnaud Mortier Aug 19 '18 at 16:05
  • $\begingroup$ @ArnaudMortier Sorry about that! I misunderstood what you were trying to convey. $\endgroup$ – Tiwa Aina Aug 19 '18 at 16:06
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    $\begingroup$ @LeAnhDung: If you offer a bounty, start small at 50 points. Don't immediately offer a lot of points because, again, getting attention (even with a bounty) is a lot of luck. $\endgroup$ – user21820 Aug 21 '18 at 10:42
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I'm not sure about appealing, but if you're looking for an answer, I think that there are some alternatives. I'm mostly just speaking from personal experience, in hopes to add to a nice list of suggestions by Arnaud Mortier.

  1. Explain succinctly the proof idea. Usually, if it is novel/ different and seems likely to work, I will usually read the rest of the question more carefully. I.e: if the proof is interesting you should mention why. Your question here I honestly would not read, because I can't see from a bunch of $\subseteq$ how anything is "bottom up" etc. This additionally will help garner comments because specialists will usually say "this will not work because of $x$.) Here, I added a single little sentence at the beginning that I think helped get a good comment that made me feel reassured and a nice answer.

  2. When the problem is localized (you are unsure about a statement or two,) put that at the top of the question and mention that you will need it to prove $xyz$.

  3. If you are just uncertain about a proof, as you were in this question, and the problem is not "localized," then just mention why you are unsure.

  4. If you are not convinced that a particular method works, ask a question in slightly greater generality. I did that here and it seemed to gather some attention (although no answer) even though I had a specific proof in mind. Basically these are along the lines of "will this type of approach work?" Questions of that sort on this sight (granted that a genuine attempt is provided) do a few things. They give answerers a little more freedom to add something interesting, open the subject matter up to a wider range of audiences, and are generally just interesting to casual readers.

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Not yet mentioned...

  1. Learn at least one formal deductive system for first-order logic (you can see my profile for one variant of Fitch-style natural deduction and some basic examples. All mathematics can be carried out in a suitably user-friendly such system, and you can mechanically check your proof for correctness. Mistakes are still possible but only due to carelessness in checking or skipping steps in the proof. I have myself caught quite a few mistakes when writing in such formal style.

  2. Try asking for help/feedback in a chat-room. The most active is of course the main chat-room Mathematics. But for logic-related stuff you can also come to the Logic chat-room. Of course, it still depends on whether people are interested and have the time to look at your stuff. =)

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