Date: Mar 22, 2013 7:10 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
WM <> wrote:

> On 22 Mrz., 21:54, William Hughes <> wrote:
> > On Mar 22, 7:24 pm, WM <> wrote:> On 22 Mrz.,
> > 16:24, William Hughes <> wrote:
> >
> > <snip>
> >
> >
> >

> > > > Infinite sets are different from finite sets
> > > > but they do not contain anything
> > > > "beyond any finite set".

> >
> > > Of course.
> >
> > We have now established that there
> > are sets that do not contain anything
> > "beyond any finite set" but
> > are different from finite sets.

> That is potential infinity.
> Actually infinite sets, however, contain something beyond any finite
> set.

They may do so but are not compelled to do so.

For example, other than in the weirdness of WMytheology, the set of all
finite naturals is an infinite set not containing anything but finite

> Consider the decimal representation of pi. It is an actually infinite
> sequence beyond any finite sequence.

But none of the digit positions of the the decimal representation of pi

WM falsely conflates the infiniteness of a set with the infiniteness of
its members,

A finite set can contain members all of which are infinite and an
infinite set can contain members all of which are finite, at least
outside the weirdness of WMytheology.
> Or consider the Binary Tree, that contains only all finite paths.

There are infinitely many finite binary trees which contain only finite
paths. But no one such tree can contain all of them.

And any COMPLETE infinite binary tree must contain infinitely and
uncountably many infinite paths and no finite paths.

> It
> is countable.

"It", being what WM claims above is "the Binary Tree, that contains only
all finite paths, does not exist outside the padded walls of
> >
> > So if you show that P is true
> > for all finite sets of natural numbers,
> > saying that there is a set for which
> > P is not true, is not a claim that
> > this set must contain something other
> > than a natural number.

> No it is a claim of foolishness.

Only inside the padded walls of Wolkenmuekenheim.

> If I prove something for all finite
> sets but say that there is a finite set for which the proof does not
> hold, then I can refrain from proving anything.

Judging by the messes that WM now claims to be his proofs, it appears
that WM is already refraining from proving anything.

> It would be nonsense
> to do so.

An act being nonsensical has not yet been sufficient to prevented WM
from performing it.