Date: Feb 21, 2013 7:14 PM
Subject: Re: Matheology � 222 Back to the roots
WM <firstname.lastname@example.org> 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
> 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!!!