On 30 Jan., 02:17, Virgil <vir...@ligriv.com> wrote: > In article > <6a9608a5-ec9c-4e81-af59-ae4caa19b...@h2g2000yqa.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 28 Jan., 22:52, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > > Now, > > > if every real has a terminating decimal representation, then... > > > I did not say that every real has a terminating representation. > > But does every real accessible real have a decimal expansion, at least > in theory?
No. > > Does every rational have a decimal expansion?
No. For instance 1/9 = 0.111... has no decimal expansion but only approximations. The limit of the increasing and converging sequence 0.1, 0.11, 0.111, ... cannot be expressed by a decimal expansion. Every attempt to produce aleph_0 digits has yet failed at a finite index. There may be infinitely many attempts. And beyond is nothing but matheology. If you believe in the existence of a decimal expansion of 1/9 in some matheological heaven, why not write it here on earth?