Date: Dec 22, 2009 9:17 AM
Author: Dik T. Winter
Subject: Re: Another AC anomaly?
In article <8baa45a8-2ba4-464b-9598-5656c43a7456@j19g2000yqk.googlegroups.com> WM <mueckenh@rz.fh-augsburg.de> writes:

> On 18 Dez., 15:22, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:

> > In article <dd852490-e622-4bc4-b858-dfcc3b142...@l13g2000yqb.googlegroups=

> .com> WM <mueck...@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 we have: Paths contain initial segments and paths are

> initial segments.

Yes, you are using "contains" with two different meanings: "be an element

of" and "be a subset of". In many cases you do not distinguish them and

that leads to misunderstandings.

> > > 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.

>

> 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.

--

dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131

home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/