In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> Am Samstag, 7. Dezember 2013 01:37:34 UTC+1 schrieb Zeit Geist: > > On Friday, December 6, 2013 2:21:02 PM UTC-7, WM wrote: > > > > > Am Freitag, 6. Dezember 2013 18:59:16 UTC+1 schrieb Zeit Geist: > > > > > > > > > > > > > > > Let d differ from r, then there is a first digit where both differ. Let d > > > differ from p, q, r, then there is a first digit where d differs from all > > > three. Let d differ from all rationals, then there is a first digít where > > > d differs from all rationals. > > > > That is incorrect. > > That is what you say when you claim that d differs from all rationals.
Note that for every n in |N there will be infinitely many rationals whose first n digits agree with d and only differ later.
So that there can never be any n such that. by digit n. d will differ from all rationals.
Nevertheless any irrational, of which even WM admits there are infinitely many, will differ from every rational in infinitely many places.
So WM could hardly be more wrong if he was trying to be.
> find only some rationals which differ from some digit whereas always, for > every n, infinitely many remain with d_1, ..., d_n is not justifying your > "all rationals are different" claim. > > > > > > > > You say for every rational q, there is a digit, where q differs from d. > > > You intentionally forget: For every rational q which is followed by > > > infinitely many other rationals, there is a first digit, where q differs > > > from d. > > > > > > > > > > > > > That is irrelevant. > > Another important reply. > > You asked at which point your quantifyer confusion appears. There are many > points one of them is this: > > You start with > A( r e Q ) E( n e N ) ( x_n ~= r_n ) > and then you switch to > E( n e N ) A( r e Q ) ( x_n ~= r_n ) > > Otherwise you would get from > A( n e N ) E( r e Q) ( x_n = r_n ) > that d with has only its d_n finitely indexed cannot differ from all > rationals. It is a rational. > > The reason for this is not irrelevant. It is the fact that A( r e Q) are not > available. > > That may be irrelevant in order to do matheology but it is not irrelevant in > mathematics. > > > Regards, WM --