```Date: Feb 25, 2013 8:49 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <a14d71fc-7e52-4731-bf9c-e2b178a88337@c6g2000yqh.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 24 Feb., 21:04, William Hughes <wpihug...@gmail.com> wrote:> > On Feb 24, 8:32 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> >> >> >> >> > > On 24 Feb., 15:56, William Hughes <wpihug...@gmail.com> wrote:> >> > > > So, when WM says that a natural number m does not> > > > exist, he may mean that you can prove it exists> > > > but you cannot find it.> >> > > > Suppose that P is a predicate such that> > > > for every natural number m, P(m) is true.> >> > > Example: Every line of the list L> >> > > 1> > > 1, 2> > > 1, 2, 3> > > ...> >> > > contains all its predecessors.> >> > > > Let x be a natural number such that> > > > P(x) is false. According to WM you cannot> > > > prove that x does not exist.  (WM> > > > rejects the obvious proof by contradiction:> >> > > >      Assume a natural number, x, such that P(x)> > > >      is false exists.> > > >      call it k> > > >      Then P(k) is both true and false.> > > >      Contradiction,  Thus the original assumption> > > >      is false and no natural number, x, such> > > >      that P(x) is false exists)> >> > > > We will say that x is an unfindable natural> > > > number.> >> > > > It is interesting to note that WM agrees with> > > > the usual results if you insert the term findable.> >> > > > E.g.> >> > > > There is no findable last element of the potentially> > > > infinite set |N.> >> > > > There is no findable index to a line of L that> > > > contains d.> >> > > > There is no ball with a findable index in the vase.> >> > > > etc.> >> > > > It does not really matter if nonfindable natural> > > > numbers exist or not. They have no effect.> >> > > > I suggest we give WM a teddy bear marked unfindable.> >> > > I suggest, William keeps abd comforts it until he can find the first> > > line of L that is not capable of containing everthing that its> > > predecessors contain.> >> > Every line of L is capable of containing everything that> > its predecessors contain.> > And why then do you believe, or at least claim, that something that is> completely in the list must be distributed over more than one line?Because for every line a part of d is not in that line.Or does WM claim that there is some line such that all of d is in that one line?  Or that there is some line in your list so that all of your list is in that one line?--
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