In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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
You just gave it one.
Every decimal expansion , finite or infinite, of a number between 0 and 1 is summation of terms Sum_(k in |N) a_k/10^k. for certain numbers a;ll but finitely many of the a_k are zero. --