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).