Re: Cantor Confusion

In article <1171981466.237613.54010@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
On 19 Feb., 15:23, "*** T. Winter" <***.Win...@xxxxxx> wrote:
....
> And if every set which contains all sets of the form {0,1,2,...,n}
> contains N,

As a subset.

Fine. Every path of the tree is a special subset. (Not every subset is
a path.) But there are only countably many finite subsets and
countably many sets of subsets which belong to one and the same path.

Yes, and so there are only countably many finite paths.

> why does the union of finite trees T(n) not contain an
> infinite path?

I have never said that. I have stated that it *does* contain infinite
paths.

So the union of finite trees U(T(n)) contains (as subsets) the path
p(oo) and all its co-paths q(oo), ..., i.e.,

Yes. I never said otherwise. Why do you think I said otherwise?
All the p(oo) are subsets of U(T(n)).

it contains P(oo)?

And that is wrong. Pray look close at what the elements of the different
sets are:
U(T(n)) has as elements nodes
P(oo) has as elements paths, i.e. sets of nodes
so P(oo) is neither an element of U(T(n)), nor is it s subset of it.
If it where an element it should be a node. If it is a subset is should
be a set of nodes, but P(oo) itself is *not* a set of nodes, it has
sets of nodes as elements.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
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