Date: Feb 21, 2013 7:14 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots
In article

<13ce0f7f-5580-456f-8db1-bd1afe7e227e@n2g2000yqg.googlegroups.com>,

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

> On 21 Feb., 20:23, William Hughes <wpihug...@gmail.com> wrote:

> > On Feb 21, 6:40 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> >

> >

> >

> >

> >

> > > On 21 Feb., 14:18, William Hughes <wpihug...@gmail.com> wrote:

> >

> > > > According to WM

> >

> > > > i.;

> >

> > > > A) For every natural number n, P(n) is true.

> > > > implies

> >

> > > that this claim A holds for every natural number from 1 to n, but not

> > > necessarily for infinitely many following.

> >

> > > > B) There does not exist a natural number n such that P(n) is

> > > > false.

>

> In fact we cannot find such a number. Nevertheless we cannot exclude

> its existence. Please consider what I wrote about the sets A and B.

> We cannot find a last finite number that has left A. Nevertheless it

> must exist.

Outside of Wolkenmuekenheim it not only need not exist, it cannot exist.

> > > Every potentially infinite set of natural numbers has a last element.

> > > But you cannot identify it.

Then no such set can exist, since in every sane set theory what WM here

claims is false.

> >

> > I do not understand. You made the claim that A implies B.

>

> For every number from 1 to n.

But not for n+1?

>

> > Now you seem to be arguing against this. Note that the statement

> > in B is that the natural number n does not exist, not that

> > the natural number n cannot be identified. I remind you again

> > that the words are yours.-

>

> The statement is that the natural number does not exist between 1 and

> n inclusively.

I do not recall that that provision *between 1 and n) was included in

the original.

>

> Find a FIS of d that is not in a line of the list or agree that you

> cannot prove that there is no natural number such that line(n) = d.

For each nth line l of lenght n,

there is a FIS_(n+1) of d having lenght n + 1.

Thus line(n) =/= d.

So unless WM has a list of lines longer than every natural, he loses!!!

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