Re: Review of Mueckenheims book.

In article <1172771927.176281.193980@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
On 1 Mrz., 03:38, "*** T. Winter" <***.Win...@xxxxxx> wrote:
....
> > > The cross section C(oo) of the union of finite trees U(T(n)) is
> > > C(oo) = |2^omega| = aleph_0.
> >
> > Proof, please. And how do you *define* C(oo)?
>
> I do not define C(oo). We are talking about the union of finite trees
> It does not contain a Level n = oo or tree T(oo).

How can you state things about things you do not define? You state C(oo)
as being something, but you do not define C(oo)?

I do not define C(oo) *starting from the complete tree* T(oo) but
using the union U(T(n)) of the finite trees, (because it is in
question whether T(oo) = U(T(n))).

So, my question remains, how do you *define* C(oo)? Until now I have not
yet seen a definition. But you are now apparently stating that
T(oo) != U(T(n))?
Because I state they are equal.


> You misunderstood. There is the saying that aleph_0 parentheses result
> in aleph_0 terms in parentheses although for every finite segment of n
> pairs of parentheses we have 2^n terms in the last pair of
> parentheses.

I can say nothing about such a saying.

The harmonic series as split off in Oresmes proof is isomorphic with
the binary tree:

I do not ask about that, I ask about the saying, and where it comes from.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.