Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Feb 2, 2013 2:32 PM
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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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