On Jan 11, 11:56 am, MoeBlee <modem...@gmail.com> wrote: > On Jan 11, 10:50 am, Dan Christensen <Dan_Christen...@sympatico.ca> > wrote: > > > They seem to > > believe that you can do serious work in group theory without any > > reference to an underlying set or even set membership. > > (I really hope > > I am wrong about this.) > > You keep saying "seem" this and "seem" that.
Just reading between lines. If I have mistaken your meaning, I apologize.
> I didn't opine as to > "serious work". > If you wish to mention my remarks, then please stick > to what I've actually said. I've asked you this a few times already. > > > They can't talk about subgroups even in the > > abstract, > > I do that, formally, in set theory, or informally in general > mathematics that includes the study of various algebras such as > groups.
But not in "first order" group theory, right? I was under the mistaken impression that its axioms with their apparently unbounded quantifiers (why bother?) were being put forward here as an alternative basis for that branch of mathematics we call group theory. What silliness!