# Definition talk:Inverse Relation

Actually, $R$ does not have to be a relation - in fact, this is the way it is most commonly addressed in literature - to have converse defined for any set, not just relations. In fact it is quite useful this way (for example, we could have that $R$ is a relation $\iff$ the converse of the converse $= R$. Same for domain and range. Would you approve this change? -Andrew Salmon 23:39, 12 September 2011 (CDT)
Well, no, it's the same thing, but without the condition that $R$ is a relation. I'm saying that the definition works for any class - not just classes of ordered pairs. -Andrew Salmon 00:48, 13 September 2011 (CDT)
Sorry - looking back on it, my response was worded terribly. It's exactly the same definition: The converse of $R = \{ < x,y > | < y , x > \in R \}$. But it's just without the proviso that $R$ is a relation (a class that contains ordered pairs only). -Andrew Salmon 01:45, 13 September 2011 (CDT)
Also note that there is already a page which proves $\left({R^{-1} }\right)^{-1} = R$ so your initial point is covered. --prime mover 03:15, 13 September 2011 (CDT)