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

<2bf7c594-8e66-4624-94d3-b1e05946811f@9g2000yqy.googlegroups.com>,

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

> contradicted.

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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