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Background: I posed a question on the main site a little over a month ago, asking if something could exist. The answer I was given was that it could not exist, and then a "proof" was given, assuming that it did exist, breaking it up into four cases, and showing that in each case we had a contradiction.

At the time of the initial posting, I didn't see anything off about it. Upon further analysis, I couldn't see how the reasoning flowed in two of them, and asked for clarification about a month back (and I did tag the answerer in the comment), but never heard back. I see the answerer on the site daily, so (unless the notification was never sent) the answerer should have been aware of my request.

Today, I finally got the chance to sit down and seriously think about it, and developed counterexamples for 2 of the 4 claims. The mistakes made were very natural and understandable, but they are mistakes.

My questions for the meta: I could make a brand new question referring to the old one and saying "the given answer is half wrong"...but that just feels rude. Is there a preferred way for me to reach the answerer to discuss this? Should I post an answer to my original question with my counterexamples (they are too long for a comment)?

Edit: Upon request (and because I can't really prevent people from going to my own profile and figuring out which post I'm referring to and who the answerer is), here is the link to the post in question: Conflicting definitions of "continuity" of ordinal-valued functions on the ordinals

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  • $\begingroup$ The answerer is very active in the main math chat room. Perhaps you can collaborate there on a solution (or in a newly created chat room). $\endgroup$
    – Bill Dubuque Mod
    Commented May 18, 2012 at 22:25
  • $\begingroup$ Could you link to the post in question? $\endgroup$
    – Arturo Magidin
    Commented May 18, 2012 at 23:24
  • $\begingroup$ @ArturoMagidin:I was trying to keep it anonymous, though apparently Bill figured it out, so I suppose I may as well. I'll edit my post. $\endgroup$
    – Cameron Buie
    Commented May 18, 2012 at 23:28
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    $\begingroup$ Your other options are: (a) edit your question to include the counterexamples, (b) if your counterexamples are existence proofs, post them as a new answer, (c) start a bounty on the question (this is only useful in conjunction with one of the other options). Do you really need to get a response from the original answerer? You might get a new answer from someone else. $\endgroup$
    – user856
    Commented May 18, 2012 at 23:31
  • $\begingroup$ The answerer is not only "very active in the main math chat room". He's become very active in the main site over the past several weeks (says the guy who used to be ranked no.1 almost every week, and now is relegated to no. 2...) I would ping him again. $\endgroup$
    – Arturo Magidin
    Commented May 18, 2012 at 23:36
  • $\begingroup$ @RahulNarain: I don't particularly need a response from the initial answerer, but I like to have things be correct if possible, and if the answerer is interested in the problem, it would provide a chance to think of an alternative approach. My counterexamples are existence proofs, yes, but not proofs of the existence of what I was looking for (though such may follow from that, I'm not sure yet). I may include the counterexamples as an edit, and if I haven't made much progress on it, I'll definitely put a bounty on it. $\endgroup$
    – Cameron Buie
    Commented May 18, 2012 at 23:37
  • $\begingroup$ @ArturoMagidin: I'll try that again. Given how active he is, I suppose it's reasonable that my notification got buried in a heap of others! $\endgroup$
    – Cameron Buie
    Commented May 18, 2012 at 23:38
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    $\begingroup$ I wish that you’d pinged me again; things happened, and I simply forgot about it. $\endgroup$
    – Brian M. Scott
    Commented May 20, 2012 at 9:53
  • $\begingroup$ @BrianM.Scott: Yeah, go ahead and chalk this whole meta post to me being somewhat socially inept. I should just have done that, from the start. Ah, well. Next time. $\endgroup$
    – Cameron Buie
    Commented May 20, 2012 at 18:39

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I think it could be beneficial to post your counterexample (to the first Answer), perhaps as a second Answer if it is too bulky to post either as a Comment or as an edit to the Question itself.

Another approach would be to create a Chat Room about the post and counterexample, esp. if the "counterexample" is not really all that germane to the original Question. Discussion might turn up a way that your example doesn't fully satisfy the assumptions/limitations imposed by the first Answer.

Not every upvoted (or even accepted) Answer is a gem of rigor and completeness. I think the criterion should be whether it is useful (and obviously things that are badly wrong or "not even wrong" would not meet that criterion). Here the first Answer seems to have involved some worthwhile insight since it advanced your own understanding. The philosophy is to incrementally improve Answers, not to obliterate all things with flaws and start over from scratch.

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  • $\begingroup$ Agreed. I certainly don't want to scrap it, and it was quite useful. I'd like to refine it and see how much more mileage I can get out of it. $\endgroup$
    – Cameron Buie
    Commented May 19, 2012 at 16:18

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