In article <firstname.lastname@example.org>, WM <email@example.com> 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.
Nevertheless every rational gets counted, just as every natural has a successor but, at least outside of WM's wild weird world of WMytheology, we have a set containing of all of them.