Date: Feb 6, 2013 4:08 AM
Author: Virgil
Subject: Re: Matheology 203
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 MÃ¼ckenheim 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 MÃ¼ckenheim, "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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