In article <firstname.lastname@example.org>, WM <email@example.com> wrote: > Am Freitag, 6. Dezember 2013 23:56:10 UTC+1 schrieb Virgil: > > > 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 digit where > > > d > > > differs from all rationals. > > Let d first differ from r1 at digit 1 > > let d first differ from r2 at digit 2 > > let d first differ from r3 at digit 3 > > ... > Then it differs at digit 3 from all three rationals. > > let d first differ from r_n at digit n > > and so on. > "and so on" means: there are always infinitely many rationals that do not > differ. Name one!
> > Then, while for every n in |N, > > d DOES differ from n rationals by line n, > > and ultimately differs from all listed rationals > Then either you can index the "ultimate" digit d_u
WM thereby claims the existence of an ultimate natural whch thus cannot have any successor natural. But this sort of thing does not occur anywhere outside of WM's wild weird world of WMytheology.
> or you cannot. In the > latter case you either have to assume a digit without natural index u
WM may have to assume such foolish things, but no one else does..
> or you have to confess that the > ultimate case does never appear.
Or one could merely asume that there is no such thing as an "ultimate case", which is what is assumed by everyone outside of WM's wild weird world of WMytheology when dealing with sets like |N.
> That is tantamount that d does never differ > from all rationals. That is tantamount to the ultimate in stupidity!
> > Actually it is WM's "proof" that, as usual, has been shown not to hold. > > See counter-proof above! > You have a strange use of language