|
|
Re: Matheology § 047
Posted:
Jun 27, 2012 3:03 AM
|
|
On 27 Jun., 05:11, William Hughes <wpihug...@gmail.com> wrote:
> On Jun 26, 3:51 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > On 25 Jun., 23:38, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Jun 25, 6:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > <snip>
>
> > > > Either x is adjacent to an interval, or it is adjacent to an
> > > > uncovered irrational.
>
> > > Or it is not adjacent to anything. (Tell me, what number is
> > > 256.57 adjacent to?).
>
> > You dismiss non-constructive proofs?
>
> No, you misunderstand. The point is not that we do not know what
> number
> 256.57 is adjacent to. The point is that there is no number that
> 256.57 is adjacent to.
I agree with this point. But if infinity is finished, then we need all
numnbers. Then x must be adjacent to something, even if we don't know
what it is. Then there must be all rationals. And that false claim is
where I start.
Take a ring of circumference 1.
In the first step construct aleph_0 pairs of endpoints in an
arbitrary
way. In a second step that we do not control and that has nothing to
do with long distance effects, let the endpoints slide and wait and
wait and wait... until they have reached the configuration of the
intervals I_n covering the rationals q_n with length 10^-n. This is
not excluded as a final state - if the I_n can brought to existence
at
all. Then tell me the moment when the aleph_0 complementary intervals
have become uncountably many singletons during this continuous
process.
Regards, WM
|
|
