Talk:Operating on Transitive Relationships Compatible with Operation

Rename

No, that's not it. The point here is really about how transitivity strengthens compatibility. The reflexive closure stuff is there because we want to prove that $a < b$ and $c \le d$ implies not only $a \circ c \le b \circ d$ but actually $a \circ c < b \circ d$, but transitivity is what lets us do that neat trick of taking the group product on both sides of two inequalities, rather than just an inequality and an equation. --Dfeuer (talk) 10:59, 12 January 2013 (UTC)

Perhaps there's a way to separate those aspects cleanly? --Dfeuer (talk) 11:00, 12 January 2013 (UTC)