User talk:Dfeuer/Cone Condition Equivalent to Reflexivity

That's interesting.... If I'm not mistaken, this actually means that every transitive relation compatible with a group must be either reflexive or irreflexive.

Let's see... If $x \mathrel{R} x$, then $x \circ x^{-1} \mathrel{R} x \circ x^{-1}$, so $e \mathrel{R} e$, from which $y \mathrel{R} y$, so that holds. I wasn't expecting that. --Dfeuer (talk) 08:28, 31 January 2013 (UTC)


 * It appears that even transitivity is not necessary. You have only used compatibility. --Lord_Farin (talk) 08:54, 31 January 2013 (UTC)