Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology 203
Posted:
Feb 6, 2013 4:08 AM
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In article
<31ec64ee-9225-4b37-86b2-4991b21af97b@hq4g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 6 Feb., 04:47, Ralf Bader <ba...@nefkom.net> wrote:
>
> > I am indeed slightly confused about what you wrote and what it has to do
> > with the previous discussion. This was centered around a "list" of decimal
> > fractions, namely:
> > To the natural number i, the fraction 0.1...100... with exactly i digits
> > equalling 1 is associated. And the assertion of Mückenheim was that
> > s=0.111... with infinitely many digits equalling 1 "is" somehow in this
> > list, because all its finite initial segments appear in the list.
>
> Everything of 0.111... that can be defined by sequences of 1's, is in
> the list. The finite definition "s" or "o.111..." is not in the list,
> but finite definitions have nothing to do with Cantor's diagonal
> proof.
> Is that really exceeding the capacity of your brain?
It certainly seems beyond the capacity of WM's.
>
> > And this I called idiotic crap, and I still do so;
>
> Lessen your blood pressure.
>
> > if I should have
> > overlooked something deeply profound, I still don't see it.
>
> Obviously.
>
>
> > According to Mückenheim, "There is no
> > sensible way of saying that 0.111... is more than every
> > FIS". Of the authorities you called upon, whom would you find capable of
> > regardng this as a sensible assertion?
>
> Brouwer said so, for instance: Every infinite sequence must have a
> repeating element. Why would that be required if not in order to
> facilitate a finite definition? But why do we need a finite
> definition?
0.111... is a finite definition for Sum_(n in |N) 1/b^n, where b is the
base in whch 0.111... is being written.
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