Despite this having been discussed multiple times:
What are the guidelines for what should be posted as an answer and what should be posted as a comment?
There should be none. Like most other things in a community forum, it is up to the users to make their own best judgements. In this case, @t.b. didn't think what he wrote deserved to be an answer, but doesn't hold that position strongly. So when poked by @Listings about it, he changed his mind. (I actually wrote the exactly the same comment as t.b. did for that question, with a poke to @sos440 to post his/her comment as an answer; I deleted that after seeing t.b. had me beaten by seconds).
<rant on cultural norms>
It is generally in the culture of Mathematicians to be more conservative about what they say: they tend to be more cautious about unqualified statements (c.f. that joke with engineer, physicist, and mathematician ending with "...there's at least one sheep in Scotland of which at least one of its sides is black"). This also leads to a lot of mathematicians snarking at physics journals publishing what they consider to be "easy corollaries of known results". This self-set high bar for what is publication-worthy may or may not have something to do with how a lot of partial answers appear as comments in this website. </rant on cultural norms>
Another possibility, besides my above rant, is that the user is only leaving a short sketch of the complete answer in the comments. For those with sufficient mathematical maturity, those short sketches may appear to be a complete answer. But for a self-conscious educator, those sketches may not be sufficiently pedagogical as an answer. Nobody, not even the great @Arturo Magidin himself can write Arturo-style expositions for every question seen. (In your second link, I would assert that by Arturo's standards, that comment is far from a complete answer...)
On the flip side, because of the Q&A (emphasis on the A part) nature of this site, we desire answers. So if a user decides to post an answer as a comment, I think he or she should not complain when somebody else decides to incorporate the content of said comment into a "more complete" answer.
Which leads to...
If you see an "unanswered question" with the answer already appearing in the comments, you can either:
- Ping the author of that comment and request that it be posted as an answer;
- Just copy the comment and post it as an answer yourself (perhaps with proper attribution, and/or marking it as community wiki if you don't want the credit); or
- Expand upon that comment and write a better, clearer answer.
