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:
And here something you may have missed this morning. You invtroduced the sequence 1 10 100 ... But it seems you are no longer interested in your argument?
> P(n): n is not the index of a position with a 1.
> P(1) is true. > If P(n) is true then P(n+1) is true.
> For each natural number n, P(n) is true.-
Great! What about the digits in the sequence 1. 12. 123. ...
In order to avoid complications with numbers > 9 consider the indices only. Here induction shows: n is not the index of a position with a finite index. According to set theory all digits vanish in the infinite. Set theory is really a theory of spirit. But analysis runs differently (see above). And say, why is the anti-diagonal yet determined in such a boring way? We could make it vanish completely. Then Cantorian disciples would come to rest.
