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In answer to my question

What are some good simple examples that getting the right result is not enough?

I was pointed to this thread on M.SE as a duplicate:

https://math.stackexchange.com/questions/260656/cant-argue-with-success-looking-for-bad-math-that-gets-away-with-it

I think that this is an excellent example for a general discussion: On the surface, the question are practically the same "Look at this example, give me similar examples.", but on a first view of the M.SE I get the impression that it would be hard to find examples there that are usable for a course.

It looks more like a collections of anecdotes "Hey, I had a student who thought that since $x^2+y^2=1$ gives a circle, $x^2+\frac 12 y^2= 1$ gives a semi-circle." which can be fun, but not really useful to present to students.

I am really not that invested in my particular question if you do not like it, but the general question is:

At what point does the expectation of a very different kind of answer here make a very similar question not a duplicate to M.SE?

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The key principle is to Respect the community – your own, and others’. There's naturally going to be some cross-over between this site and Math.SE. But this site has a different focus and therefore a different audience than the mathematics site. A critical part of the beta (especially during the private beta) is to establish this communities unique culture. Lot's of sites on Stack Exchange have natural affinities with other sites, so it's really not unusual to have very similar questions asked on two or more sites.

If a question is asked on Astronomy and Physics, we expect to find answers appropriate to astronomers on one and more general physicists on the other. On Math.SE, I expect to see answers from people who use mathematics. On this site, I expect to see answers from people who teach mathematics. Those people are often the same individuals and the difference might be subtle, but establishing your own culture is something to strive for.

Answers might link, quote, and heavily borrow from answers on other sites. But there should be some way to give an answer unique to Mathematics Educators. If not, that might be a sign the question is not really on topic.

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