Talk:Relation Compatible with Group Operation is Reflexive or Antireflexive

Both being possible

I don't really understand why we need to show here thatr it's possible for a compatible relation to be reflexive and that it's possible for one to be antireflexive. All this aims to do is show that it must be one or the other. Trivial examples of each: The trivial relation $G\times G$ is trivially reflexive and trivially compatible. The empty relation $\varnothing$ is trivially antireflexive and vacuously compatible. --Dfeuer (talk) 21:46, 16 September 2013 (UTC)

In order to put this result into context, it would be useful to find a non-trivial example of each. Just because you "don't really understand" why there is that potential room for improvement does not mean that such a nugget of information should not be included. --prime mover (talk) 05:23, 17 September 2013 (UTC)

Non-trivial examples abound: Every congruence relation or compatible ordering on a group is a reflexive example, and every compatible strict ordering is an antireflexive example. How do you propose to select appropriate examples? --Dfeuer (talk) 20:00, 17 September 2013 (UTC)

Well, I hadn't thought about it. I just thought it would be a useful addition to the page. Feel free to come up with something that would fit the bill. If you don't want to do it, then nobody's forcing you to. Come to think of it, nobody even actually asked you to. --prime mover (talk) 20:03, 17 September 2013 (UTC)