In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> > No, you use "up to every finite digit there are infinitely many rationals > > identical with d up to that digit." To show "by digits it is impossible to > > prove that d differs from all rationals" > > by digits that have a finite index. Please don't forget that.
All the digits of d have finite indices, at least everywhere outside of WM's wild weird world of WMytheology.
But also, for every d_n, d was constructed so as to from d_n at digit n in such a way as to avoid any double representation problems, so we can require d in position n to be which ever of digits 5 or 6 d_n is not equal to in its position n.
> usually claims the handwaving "infinite sequence"
If the d_n were not an infinite sequence of rationals, or the d_n an infinite sequence of digits, we would be back in the wilds of WMytheology.