I just read https://lukepalmer.wordpress.com/2013/03/25/follow-your-nose-proofs/, and realized that "follow your nose proofs" were already analyzed by Dijkstra/Scholten/Feijen/Gries in the context of their distinctive proof style and format. They call such proof "there is only one thing you can do", under the slogan "let the formulae do the work". (See my answer https://math.stackexchange.com/a/332186/11994 for an example and some references.)

So as a way of spreading knowledge about this proof style, I'd like to post Dijkstra-style proofs for Luke Palmer's two examples on this site.

Now, I'm thinking about posting a question, "How are 'follow your nose proofs' handled in Dijkstra et al.'s proof style?" and adding an answer with the two example proofs.

My question: Is this type of self-answered question appropriate here? If not, in which appropriate form could I post these examples here?

  • $\begingroup$ Why the -1? Is it inappropriate to ask about the appropriateness of a question? Please add a comment if you vote down... Thanks! $\endgroup$ – Marnix Klooster Mar 29 '13 at 10:16
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    $\begingroup$ Votes on meta have a much broader range of interpretation on meta than on the main site. The downvote could simply be a disagreement to the appropriateness of such a question on the main site (and not the appropriateness of asking on meta about the appropriateness of such a question on the main site). $\endgroup$ – user642796 Mar 29 '13 at 10:20
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    $\begingroup$ @ArthurFischer Thanks! (And upvoted that comment, since that seems to mean the same thing here. :-) $\endgroup$ – Marnix Klooster Mar 29 '13 at 10:25

It doesn't sound like an appropriate question to me.

It is OK in general to ask questions for the purpose of answering them, but the question must still be a real question -- that is, something that one could imagine someone who doesn't know the answer could explicitly desire to find out.

Your proposed question seems to fail that test -- it sounds too artificial, too much like a question whose only reason to be asked by anyone is to give someone an excuse to speak up with the answer you want to provide.

The thing about nose-following proofs is that they are not very interesting. They need to be taught to students, of course, because everyone needs to be able to do them automatically and effortlessly such that one can spend one's mental effort at the interesting cases where the nose leads nowhere. Singling them out as a class with a cute name seems to be mostly for the purpose of driving home to students that "prove this-or-that" is not necessarily a matter of a creative idea or deep insight, while also avoiding the misconception that all proofs are something one can expect to find by simply following a mechanistic procedure.

But I cannot imagine anyone wondering how exactly this kind of simple, straightforward proofs are dealt with in some particular style of proofs that they otherwise knows nothing about. And if they know something about that style of proofs, shouldn't that something include at the least how to write the easy parts of a proof in that style?

  • $\begingroup$ I'd be interested in seeing the opinions of the downvoters stated in a bit more detail. Which part(s) of the answer do they disagree with? $\endgroup$ – Henning Makholm Apr 1 '13 at 17:11

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