```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 elementof" and "be a subset of".  In many cases you do not distinguish them andthat 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, +31205924131home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/
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