In article <Kv251u.sI@cwi.nl>, "Dik T. Winter" <Dik.Winter@cwi.nl> wrote:
> > The union contains subsets. > > > > > > This is so according to set theory. Of course it is rubbish. > > > > > > Well, if you want to use terminology in a different meaning than > > > standard, of course. > > > > To contain as a subset is not correct in English? > > It is correct English but misleading in a set theoretic context.
A set can contain something as a subset OR contain something as a member, but these are different containment relationships, neither of which necessitates the other.
WM has the bad habit of using "contain" ambiguously. It often seems that he is being purposely ambiguous about it.
Proper mathematical usage requires that "contain" be used unambiguously, whenever there can be any doubt, by explicitly stating in each such instance whether it means the subset or the membership relation.