On 30 Jan., 09:47, Virgil <vir...@ligriv.com> wrote: > In article > <4a768b6d-0d71-4e89-bf77-6b70d6e5e...@d11g2000yqe.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> 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. > No. I know, it is very unfamiliar, but it is fact: "0.111..." is not a decimal expansion. For instance, because decimal expansions by definition have only one point. 0.111... is a finite definition of 1/9 like 1/9 is itself. It formulates a task, namely to find the n-th digit of the decimal expansion. This task can be accomplished for every n, but not for all.