On 23 Nov., 15:42, William Hughes <wpihug...@gmail.com> wrote: > On Nov 23, 10:32 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 23 Nov., 15:16, William Hughes <wpihug...@gmail.com> wrote: > > > > On Nov 23, 10:11 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 23 Nov., 13:27, William Hughes <wpihug...@gmail.com> wrote: > > > > > > So to summarize: > > > > > > Analysis: > > > > > limit in real numbers: unbounded > > > > > (oo in extended reals) > > > > > > limit of set of 1's: > > > oo = Limit[n-->oo] SUM[k=0 to n] 10^k > > = 1*10^0 + 1*10^1 + 1*10^2 + 1*10^3 + ... > > = ...111 > > this piece of nonsense has nothing to do > with the limit of the sequence > > 1 > 10 > 100 > ... > > which is oo = Limit[n-->oo] 10^k > and it not represented by any numeral.
That is of little interest! You want to excuse one mistake by another one.
The sequence 1 11 111 ... with its limit oo = Limit[n-->oo] SUM[k=0 to n] 10^k = 1*10^0 + 1*10^1 + 1*10^2 + 1*10^3 + ... = ...111 is represented by digits. So is my original sequence. The number of digits is oo when calculated by analysis, but 0 when calculated by set theory. This is one contradiction. And in mathematics one contradiction is sufficient to run a proof by contradiction.
