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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