In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> Am Montag, 9. Dezember 2013 22:01:18 UTC+1 schrieb Zeit Geist: > > > > > I am not interested in your "proofs" but in defining an irrational number > > > like the antidiagonal d by an arbitrarily large sequence of its digits > > > d_n (including an infinite sequence). This is impossible because for > > > every digits d_n there are infinitely many duplicates. > > > > > > > > > > > > > You not interested in any proofs at all. You shout Dogma. > > > > > > > > The above "proof" is invalid, but you are even too blind to that. > > I see that it is in agreement with mathematics
Then you see what is not there.
> For every finite or infinite > sequence of digits of d there is a rational number including it.
Since there is no reason to suppose that d is an ultimately repeating sequence of digits and a good deal of reason to suppose otherwise, it must obviously differ in that respect from any sequence of digits which IS ultimately repeating, which includes each and ever and all rational .
So that WM is claiming that any sequence of digits which is not ultimately repeating must somehow equal some sequence of digits which is ultimately repeating. Othewise there will be sequences of digits not included in a listing of all sequences representing rationals.
That can be and has been proven. That is of more value than WM's "proofs" which lead to obviously false results.
> > > > > > The Logic in that above exposition resembles the flawed reasoning you would > > use. > > > But it leads to the correct result: It is impossible to distinguish d by its > digits from all entries of arationals-complete list. > > Regards, WM --