```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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