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Topic: Matheology § 198
Replies: 40   Last Post: Jan 26, 2013 6:54 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 198
Posted: Jan 25, 2013 3:00 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 25 Jan., 09:26, Virgil <vir...@ligriv.com> wrote:
>

> > > How do you express actual infinity by means of nodes or levels?
> > > Try it.
> > > Write a sequence like xxxxxxxxxx... and do never stop.

> >
> > It is the knowledge that it never stops that makes it NOT FINITE.

To have extra knowledge beyond what WM has is a necessary qualification
for every true mathematician, and a lot of non-matjematicians, for that
matter.
>
> Yes you need some external "knowledge" or better say trust in
> matheology.

If "matheology" is what goes on outside Wolkenmuekenheim, we should all
learn it.
>
> > It is also the knowledge that no finite initial segment of natural
> > numbers (fison) surjects onto it that makes it infinite.

>
> That is correct in every case. The reason could be that N does not
> exist as something completed.

It exists as a completed idea, which is a much existence as anything
purely mathematical has.
> >
> > > Tell me when you have expressed an infinite sequence.
> >
> > Tell me when you can surject a fison onto it.

>
> I am fairly sure that I can surject a FISON on that sequence that you
> may have produced today, even if you have started very early.

WM is often fairly sure of his ability, but his claims far exceed his
grasp of mathematics.
> >
> >
> >

> > > > We can use the same set of nodes to make two collections of
> > > > sets of nodes. One collection contains all sets of nodes, X, with
> > > > the property that there is a node in X with a level greater or
> > > > equal to that of any other node in X.
> > > > The other collection contains all sets of nodes, Y, with the property
> > > > that there is no node in Y with a level greater or equal to that of
> > > > any other node Y.

> >
> > > No. You cannot express the latter by nodes and levels. If you don't
> > > believe me, try it.

> >
> > We have already done so to our own satisfaction, by showing that no
> > fison surjects onto any a path ( as a sequnce of nodes) in a real
> > Complete Infinite Binary Tree

>
> So the complete infinite paths must extend beyond every finit path in
> the tree?

Just like |N exceeds every FISON.

|N is essentially a Complete Infinite Unary Tree.

And if the tree contains only all finite paths, then we have
> something like the bed of Procrustes. What shall we do? Cut the tails
> that are too long? I would be glad to do so, but I have never seen
> any. Perhaps it is only an apparition of matheology if you see such
> tails?

Just as outside of Wolkenmuekenheim there can be a union of all FISONS
which is an infinite path in a Complete Infinite Unary Tree, unions of
nested sequences of finite sets of rooted node chains form paths .
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