On Tuesday, December 3, 2013 1:13:26 AM UTC-7, WM wrote: > 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. >
And there are Infinitely many Even Numvers following Every given Even Number. However, we can still find a Bijection between the Set of All Even Numbers and the Set of All Natural Numbers.
Also, if you don't think all the Rationals are counted (removed), please name at least one specific example that is Not Counted (removed).