Re: Review of Mueckenheims book.

On 22 Feb., 19:30, "MoeBlee" <jazzm...@xxxxxxxxxxx> wrote:
On Feb 22, 5:08 am, mueck...@xxxxxxxxxxxxxxxxx wrote:

On 21 Feb., 21:50, "MoeBlee" <jazzm...@xxxxxxxxxxx> wrote:

Are you talking about Skolem's paradox now? First, what identity
mapping are you referring to? There always exists a bijection of a set
onto itself. As to other mappings, they exist or they don't as
provided by the axioms of the theory. And we have to be careful to be
specific as to what requirements we place as to in WHICH sets a
mapping does or does not exist.

In any model of ZFC: With the empty set there exists the set omega and
with it is power set, and with it the identity mapping of the power
set onto itself

It is not excluded "a priori" that a model of ZFC might not map '0' to
the empty set, 'w' to omega, or even 'e' to the membership relation.

Every model of ZFC has the empty set, has omega and has P(omega) let
alone the "element of" relation. Otherwise it is not a model of ZFC
including the three important axioms.

Anyway, the identity function on the power set of omega is a bijection
from the power set of omega onto the power set of omega, yes, we know
that.

And if there is a model of ZFC without this identity function, then
this raises the question, whether this identity function is in other
models. Every set theorist believes that the identity mapping of R
exists in current mathematics - perhaps without reason?

ZFC is not a theory of physics. I don't know much about the Tarski-
Banach theorem, but I have not read that it entails anything contrary
to physics. As I understand, the theorem does not render that a
PHYSICAL object may be perform in the way the ABSTRACT object in the
theorem performs.

It is about geometry. Geometry is about physics.

Geometry is USED for physics. That does not entail that all geometry
has a direct object-by-object correlation with physics.

Geometry is developed from physics and can be applied to physics.

If the dissection as
proven possible by Banach and Tarski (but, of course, not concretely
defined --- see well ordering of the reals) could be applied in
geometry, then it could be applied in physics.

Only you could say how YOU would apply it. Meanwhile, other people are
free not to apply it the way YOU apply it.

I can apply it. And if I knew the trick of Banach Tarski (if they
themselves knew it which they don't) then we could make money or
distroy the world or do whatever is desirable or undesirable.

Obviously this result
of set theory contradicts set theory (more precisely: the axiom of
choice) for anybody who is not a strong believer without a critical
sense or the wish to accept the truth.

More empty rhetoric by you. No P and ~P in set theory do you adduce.

P: X is one ball. ~P: X is not one ball. That is a contradiction.
There is no need to dig deeper.

As far as I remember you wanted to do some proofs
concerning the binary tree, which from my diskussion with *** should
be clear to anybody.

There've been a lot of posts I've made to you regarding things other
than your tree. I wasn't talking about the tree. But as to the tree,
you completely miss my point about that, even as I BELABORED it: I was
willing to discuss your tree argument with you IF you would give me
the courtesy of FIRST telling me what the ground rules are,
specifically whether you were claiming to work strictly in a Z set
theory

If you will work on it, you may do it in ZFC.

I for my part see that every path existing in the tree cannot exist
without an edge where it splits off from the rest of the tree,
whenever it splits off. Hence there cannot be more paths than edges,
or in other words: the number of existing paths is not larger than the
number of edges.

This reasoning is basic to thinking and prior to any theory like ZFC.


Regards, WM

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