Talk:Inversion Mapping on Ordered Group is Dual Order-Isomorphism

From this and your result, it looks like we get a very strong, but hard to describe, fact that the inversion mapping on an ordered group is an order isomorphism and a group isomorphism to the opposite group with the dual ordering. --Dfeuer (talk) 23:45, 22 February 2013 (UTC)

Describing it requires a definition of a "dual ordered structure". Incidentally that result will have as a corollary that $(\R,\le) \to (\R,\ge), x \mapsto -x$ is an order isomorphism. But I advocate some literature search first before advancing in that direction. — Lord_Farin (talk) 08:42, 23 February 2013 (UTC)