Am Dienstag, 3. Dezember 2013 04:02:09 UTC+1 schrieb Zeit Geist:
> > > I start with the enumeration: 1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1, ... The numbers q_n are always in the intervals already added. > > > > > > > Then each rational is eventually counted at some time. > > Yes, at each step your Set is infinite.
So you speak of the limit after all finite steps? > > However, for some step, each rational is counted (removed). > > Thus, every rational is counted.
No You forget the decisive condition: Every rational *which is followed by infinitely many uncounted rationals* is counted at some time. This holds also for the limit since there is no last rational. I do not understand why you blind yourself (eyes wide shut) to intentionally forgetting this condition.