Re: Cantor Confusion

On 11 Mai, 15:20, William Hughes <wpihug...@xxxxxxxxxxx> wrote:
On May 11, 8:31 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:





On 11 Mai, 13:31, William Hughes <wpihug...@xxxxxxxxxxx> wrote:

On May 11, 4:57 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:

On 10 Mai, 23:03, William Hughes <wpihug...@xxxxxxxxxxx> wrote:

Note: you can enumerate an infinite set of nodes.

Let us assume that.

For every node n belonging to the set of nodes that you can enumerate,
one path p'(n) is sufficient to accompany p up to that node.
p'(n) is not the same for every node.

For which node is another path required?

p(1) is not identical to p. Thus there exists a node,
call it M_1, where p and p(1) branch in different directions.
Thus, the first node at which another path is requrired
is node M_1+1.

The first node at which another path is required depends on the
choice of p(1) and what is more, given k equal to any natural number
greater than 1, you can choose p(1) to have M_1+1 = k.
What is more, given p(1), you can compute M_1+1, and find
another path, p'(1), with M_1'+1 > M_1 +1.
What is more, given p'(1), you can find
another path, p''(1), with M_1''+1 > M_1' +1.
What is more, given p''(1), you can find
another path, p'''(1), with M_1'''+1 > M_1'' +1.
You can continue this, ad infinitum, however,
at each step you have a first node at which a different
path is required.

Deciding not to respond directly to this, Muekenhiem
simply asserts:

And at each node you have a path p* with p that is the same from the
beginning and remains so forever (if there is a forever).

At each node you get a path that is with p up to that node.

Why should I use that path for any applications?

However, at no node do you get a path that remains with p forever.

Then there must be a node wat which p is single. Otherwise from all
the nodes at which p is not single, we form a sequence of nodes which
is p*.
(p" is not equal to p)
So there must be some node at which p" changes.

p* is that path which consists of all the nodes at which p is not
single (so that there is also another path). Is it impossible or
forbidden by ZFC or third order logic or pink elephants to construct a
path p* from this set of nodes? Which nodes are available for path
construction?

Regards, WM

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