Date: Dec 18, 2009 9:22 AM
Author: Dik T. Winter
Subject: Re: Another AC anomaly?

In article <dd852490-e622-4bc4-b858-dfcc3b142f8c@l13g2000yqb.googlegroups.com> WM <mueckenh@rz.fh-augsburg.de> writes:
> On 17 Dez., 20:49, Virgil <Vir...@home.esc> wrote:
...
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > No. Suppose we have the paths 0.000 and 0.100, what is their union?
> > > > And is it a path?

> >
> > > No. But the union contains two paths. And an infinite union of that
> > > kind may contain the path 0.111...

> >
> > So according to WM a union of sets may contain an object not contained
> > in any of the sets being unioned.

>
> For paths and initial segments to contain and to be is the same.


Eh? paths contain nodes and initial segments contain numbers.
But be aware that you use the word 'contains' with two different meanings
at different times.

> For paths and initial segments to contain and to be is the same. In
> fact:
> {1} U {1, 2} U {1, 2, 3} U ... = {1, 2, 3, ...}
> and also
> {1} U {1, 2} U {1, 2, 3} U ... U {1, 2, 3, ...} = {1, 2, 3, ...}.


In the mathematical sense the union contains numbers, not sets.

> 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.
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/