Re: Review of Mueckenheims book.

In article <1175944821.407579.166340@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
On 2 Apr., 15:02, "*** T. Winter" <***.Win...@xxxxxx> wrote:
....
> When showing the flaws in set theory I used the terms in their
> standard meaning. A node, an edge, a path, and a binary tree are well
> known notions.

Not from set theory, but from graph theory. But you do *not* use the
standard terminology from graph theory. You have some notion about them
that you can not (or want not) to make clear. And every attempt by others
to give set theoretic definitions of your terms is ignored by you, you
rather wish to use your ill-defined terms.

It is clear, to everybody who does not refuse to see it, that there
are not less nodes than separated paths.

And when asked for a proof you provide none. You only state: "it is clear".

Concerning your position, you
could also claim that in the *infinite* sequence 21212..., there are
more 2's than 1's (or the other way round). That would make as much
sense as the claim that there are more separated paths than nodes in
the tree.

Depends on how you define "more". As in the first case I see no definition
of it, it makes indeed no sense. In the second case there are proper
definitions that, when they are applied, indeed give the result. But as
you do not care for definitions, only for intuitistic notions, discussion
is futile.

> This is one of the realms where Georg Cantor is the undisputed master.
> I learned from his splendid and unsurpassed definition. I can' t do
> better than he - all my due efforts are in vain. Therefore I cannot
> but refer you to him:

Pray indicate where in his statements below he gives the definition of
a *potential infinite set*?

He explains the notion "potential infinity". As "sets" in set theory
are always actually existing, it is impossible for set theorists to
understand the meaning of a potentially infinite set.

Yes, so that is why I ask for a definition when you use the term. As you
are unwilling to state such a definition...

> You must try to understand him. If you cannot understand him, then I
> cannot help you. (But most of my students do understand.)

I understand him well enough. He is *not* talking about a potential
infinite set. Where in the quotes above does he use the word "Menge"?

in der Analysis haben wir es nur mit dem Unendlichkleinen und dem
Unendlichgroßen als Limesbegriff, als etwas Werdendem, Entstehendem,
Erzeugtem, d.h., wie man sagt, mit dem potentiell Unendlichen zu tun.
Aber das eigentlich Unendliche selbst ist dies nicht. Dieses haben wir
z.B., wenn wir die Gesamtheit der Zahlen 1,2,3,4, ... selbst als eine
fertige Einheit betrachten [David Hilbert: Über das Unendliche, Math.
Ann. 95 (1925) p. 167]

We have the potentially infinite set N if we do not consider N as a
"fertige Einheit". Then N is lim[n-->oo] {1,2,3,...n}.

By what *definition* do we have that "potentially infinite set"? And,
*how* do you define that limit? You are again confusing infinity from
analysis with infinity from set theory. They are *not* the same.
--
*** 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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