In article <585c28bc-8437-412d-887f-61bd29c77ccb@p17g2000vbn.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 23 Nov., 08:22, Virgil <vir...@ligriv.com> wrote: > > In article > > <cb8c0679-6c2d-4f07-8fcb-2144eaf39...@k20g2000vbj.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 23 Nov., 03:20, Virgil <vir...@ligriv.com> wrote: > > > > > > > Analysis gives a result. Set > > > > > theory gives another result which is incompatible with analysis. > > > > > > But if so, they are dealing with different questions. > > > > > They are not dealing with different questions but with one and the > > > same: What is the number of digits left to the point in the limit of > > > the infinite real sequence determining this limit uniquely. > > > > > > > 01. > > > > > 0.1 > > > > > 010.1 > > > > > 01.01 > > > > > 0101.01 > > > > > 010.101 > > > > > 01010.101 > > > > > 0101.0101 > > > > > ... > > > > The numbers of digit positions to the left of the points appears to be > > given by the sequence 2, 1, 3, 2, 4, 3, 5, 4, ... > > And that sequence has no limit at all. but is merely unbounded above. > > That's why in analysis the number of digits is unbounded (and larger > than 0).
The trouble is that there is no such decimal numeral, or other radix based numeral, which is unbounded. Every such numeral must have a first digit and only finitely many preceding its radix point.
At least in standard mathematics.
What WM may allow to go on in his Wolkenmuekenheim has no effect on what is allowed in standard mathematics. --
