In article <49b3cb68-22ab-423a-ac87-048870090005@w1g2000vbx.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 23 Nov., 22:19, WM <mueck...@rz.fh-augsburg.de> wrote: > > > in any case the limit of my sequence > > > > 01. > > > > 0.1 > > > > 010.1 > > > > 01.01 > > > > 0101.01 > > > > 010.101 > > > > 01010.101 > > > > 0101.0101 > > > > ... > > > > has infinitely many digits right to the point as well as left to the > > point. > > This can be proved by attaching pairs 01 of digits always from the > left and from the right side in a symmetrical way: > > 01. > 01.01 > 0101.01 > 0101.0101 > ... > > The overall behaviour of the digits (not of the indices) is the same > as that of the original sequence. > The sequence .01 .0101 .010101 .01010101 ... has limit 1/99, which is finitely expressible both as a repeating decimal and as a rational number, but that does not mean that either
