Date: Feb 2, 2013 2:32 PM
Author: Virgil
Subject: Re: Matheology � 203
In article

<51f0f15b-287f-4896-ade3-60af25d85499@9g2000yqy.googlegroups.com>,

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

> On 2 Feb., 09:57, fom <fomJ...@nyms.net> wrote:

> > On 2/1/2013 9:48 AM, WM wrote:

> >

> >

> >

> >

> >

> > > On 1 Feb., 16:35, William Hughes <wpihug...@gmail.com> wrote:

> > >> Let P(n) be

> > >> 0.111... is not the nth line

> > >> of

> >

> > >> 0.1000...

> > >> 0.11000...

> > >> 0.111000...

> > >> ...

> >

> > >> Clearly for every natural number n

> > >> P(n) is true.

> >

> > >> This means there is no natural

> > >> number m for which P(m) is true.

> >

> > >> It is not simply that we cannot find m,

> > >> we know that m does not exist.

> >

> > > More. We know that P(n) = 0.111... = 1/0 does not exist as an

> > > actually infinite sequence of 1's.

> >

> > Hmm....

> >

> > As I watch you make these arguments, it occurs to me...

> >

> > What proof do you have that some sequence is not infinitely

> > long?

>

> Even with no regard to Tristram Shandy who disproves actual infinite,

> we can say: The sequence for 1/9 = 0.111... cannot have indices that

> differ from all indices of its finite approximations. So you cannot

> distinguish 0.111... by looking at digits from its finite

> approximations. And you cannot use it in any discourse because every

> message is finite and needs an endoffile signal to be meaningful.

Either the sequence 0.111... has a last digit or beyond each digit

there is another. Tertium Non Datur, at least not outsiede WMytheology .

>

> Concluding: The property that a sequence of digits does not end cannot

> be obtained from its digits. (Remember, 0.111... is not a sequence of

> digits but is only a rule to construct a sequence of digits. The rule

> yields the sequence, but the sequence does not yield the rule.)

>

> That means in mathematics

WM is incompetent to speak for mathematics.

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