Definition talk:Inverse of Subset

This is confusing. Is it really supposed to be cancellable elements or only invertible ones? If just cancellable, the set of left inverses of elements of $X$ can be different from the set of right inverses, no? --Dfeuer (talk) 19:42, 4 February 2013 (UTC)

PM, do you have any sources for the monoid definition other than the one exercise in Warner? For the reason above, it strikes me as shaky. To compound the shakiness, not every cancellable element even has a left or right inverse, so cancellability only implies that no element has more than one inverse in the inverse subset. --Dfeuer (talk) 20:35, 4 February 2013 (UTC)