On 9 Jan., 00:15, Virgil <vir...@ligriv.com> wrote: > In article > <99114492-6fad-4ac1-a30e-ff70224ad...@c14g2000vbd.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 8 Jan., 14:44, mstem...@walkabout.empros.com (Michael Stemper) > > > > However, ANY real can be distinguished from ANY other by SOME finite > > > initial segment of its decimal, or other base, representation. > > > The problem is not distinguishing given reals, but how reals can > > uniquely by *given*. That requires a finite definition. But I am > > afraid that you don't even understand what that means.
> A set is determined by any rule for distinguishing whether a test object > is or is not a member.
A real number is determined or "given" by a unique word. Otherwise it could not be used. And it was not possible to compare some finite initial segment of it with something else.