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?
> 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.
These fractions > and the list are a pretty simple matter, and I really do not see why the > help of Wittgenstein, Russell, Quine, Goedel, Jech and Robinson is required > to find out what is "in" that list.
Try to find out what of 0.111andoson is not in the list.
> 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?