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Re: Matheology § 047
Posted:
Jun 26, 2012 3:50 PM
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On Jun 26, 10:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 26 Jun., 01:12, FredJeffries <fredjeffr...@gmail.com> wrote:
>
> > On Jun 25, 2:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > I am not interested in a special interval. I_n stands for any
> > > interval. Either x is adjacent to an interval, or it is adjacent to an
> > > uncovered irrational. That are the two options put by tertium non
> > > datur.
>
> > Consider the set of open intervals of the non-negative real axis:
> > { (1/(n-1), 1/n) | n a positive natural number }
>
> > Please tell us which interval or which point 0 is adjacent to.-
>
> I have no constructive proof, but a non-constructive disproof. Here it
> is: 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.
A train leaves Munich at a completely arbitrary time. It
travels on a track at a randomly varying speed, the switches
are randomly changed at completely arbitrary times.
Tell us what time the train arrives in Hamburg.
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