Date: Feb 21, 2013 3:51 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

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

> On 20 Feb., 23:27, William Hughes <wpihug...@gmail.com> wrote:
>

> >
> > > > For every natural number n we have
> > > >     the nth line of L and x
> > > >     are not coFIS

> >
> > > > true?-
> >
> > > True
> >
> > Is the statement
> >
> > There is no natural number m
> > such that the mth line of L and x
> > are coFIS
> >
> > true?-

>
> No, the statement is wrong. The true statement is: We cannot find the
> largest number such that the mth line and x are coFIS. Again you
> assume actual infinity for x.
>
> Consider the union of ordered sets in ZF:
> (1, )
> (1, 2, )
> (1, 2, 3, )

While I am aware of sets in ZF standardly used to represent 1,2,3, and
so on, and even 0, I am not aware of any set in ZF that represents a
blank. And everything in ZF is a set, so without such a set there cannot
be a blank in ZF.
>
> Each set has a blank.

Not in ZF. WM goofs as usual!
>
> Or consider the union of natural numbers in a set B while there
> remains always one number in the intermediate reservoir A.
>
> A B
> --> 1 -->{ }
> --> 2,1 -->{ }
> --> 2 -->1
> --> 3, 2 -->1
> --> 3 -->1, 2
> --> 4, 3 -->1, 2
> --> 4 -->1, 2, 3
> ...
> --> n -->1, 2, 3, ..., n-1
> --> n+1, n -->1, 2, 3, ..., n-1
> --> n+1 -->1, 2, 3, ..., n-1, n
> ...
>
> One would think that never all naturals can be collected in B, since a
> number n can leave A not before n+1 has arrived.
>
> Of course this shows that ZF with its set of all natural numbers is

WM's A and B are not sets but sequences of sets, so if WM wants to
consider a limit to any such sequences, he must first define what he
means by such a limit, as there is no universal definition for "the"
limit of a sequence of sets.

> Presumably it is this recognition that raises your
> interest in potential infinity of analysis.

WM's presumptions are again wrong.

> Therefore the set
> 0
> 10
> 110
> 1110
> ...
> has a line that is coFIS with 111... (up to every n - and more is not
> feasible).

Only in WMytheology.

Everywhere else a line containing 0 can never be coFIS with a line not
containing 0.
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