On 2 Nov., 14:27, William Hughes <wpihug...@gmail.com> wrote: > On Nov 2, 3:43 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 2 Nov., 01:30, William Hughes <wpihug...@gmail.com> wrote: > > <snip> > > > > In any case complete strings of digits (one digit for every natural > > > number) do carry mathematical meaning. Take, e.g. 0.111... > > > This is by definition the limit of the partial sums > > > > S= > > > 0.1 > > > 0.11 > > > 0.111 > > > ... > > > > This limit is 1/9. > > > Yes, of course. But it is not realized by digits. > > There is a string, not in S, which represents 1/9. > This string consists of digits. Whether or not this means that > 1/9 is "realized by digits" I don't know.
But we just proved it. Recently you knew it.
> However, the fact that > the complete string of 1's represents 1/9 means it has mathematical > meaning.
No, it is just imprecise abuse of mathematicsl language. We know that the sequence does not contain its limit. You assume that the series does contain its limit. But the series is nothing but a sequence (of its partial sums).
