In article <email@example.com>, WM <firstname.lastname@example.org> 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. --