Re: Review of Mueckenheims book.

In article <1175414164.124088.100300@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

On 30 Mrz., 05:27, "*** T. Winter" <***.Win...@xxxxxx> wrote:
In article <1175190711.475562.138...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
mueck...@xxxxxxxxxxxxxxxxx writes:

> On 29 Mrz., 16:55, "*** T. Winter" <***.Win...@xxxxxx> wrote:
>
> > > I said already several times: There is no potential infinite set
> > > with
> > > the meaning of "set" according to set theory, because every set
> > > according to set theory is actually infinite.
> >
> > Why then did you *use* that term?
>
> Because set theory has no copyright on the word "set". There are
> potentially infinite sets like N. But theese are not sets in the sense
> of set theory. Read chapter 10 of my book. There I explain the meaning
> of the real set of natural numbers.

And that is why I have so much problems with that chapter. Your use of
standard terms without standard meanings.

However, you did use that term to show flaws in set theory. If you want
to show flaws you should conform to the theory or either be misunderstood.

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.

Then WM is claiming that infinite trees are not infinite trees.

But it is easy enough in either ZF or NBG to model such a tree, for
example:

Let N = {0,1,2,3,...} be the von Neumann naturals, so that for each n e
N, n = {m e N: m e n}.

Then every ordered partition (L,R) of n denotes a node of level n, that
node reached by branching left or right at level m according to whether
M is a member of L or R.

The number of nodes at level n equals the number of ordered partitions
of N which equals Card(P(n)) = 2^n.

For the root node one has L = R= {}
For the root's left child one has L= {0}, R= {}
and the root's right child one has L= {}, R= {0}


At the next level one has the 4 grandchildren
({0,1},{}) and {({0},{1}) and ({1},{0}) and ({},{0,1}).

and so on.

Thus at level n there are 2^n nodes, the cardinal of the power set of
N_n = {0,1,2,...,n-1}

Then A path in such a tree is merely a similar partition of N into an
ordered partition of N itself.

Now can WM find any reason why this model does not satisfy any
requirement of treeness?

Except, of course, that it proves him wrong.







In chapter 10 I do not refer to standard set theory but
to reality and real mathematics which I call MatheRealism.


But by conflating meaningsbetwe mathemtics and WMetics, WM only creates
MatheChaos.

I am still wondering why, when I asked you for a definition of "potential
infinite set" you referred to your page on wikipedia which does not contain
such a definition at all.

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:


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

If you present it to them only in a language which they understand
poorly if at all, they will not understand it.

And it is Not Cantor's notions which we object to but WM's, especially
when he chooses to obfuscate instead of clarify.
.

Quantcast