On Jan 4, 5:33 am, Virgil <vir...@ligriv.com> wrote: > In article > <6302ee90-f0a2-4be5-9dbb-c1f999c3a...@c16g2000yqi.googlegroups.com>, > > Zuhair <zaljo...@gmail.com> wrote: > > Since all reals are distinguished by finite initial > > segments of them, > > Some reals are distinguished by finite initial segments of their decimal > representations, most are not. >
r is distinguishable on finite basis iff For Every real x. ~x=r -> Exist n: d_n of r =/= d_n of x.
As far as I know every real is so distinguishable.
In your version you changed the quantifier order, your version is speaking about the following:
r is distinguishable on finite basis iff Exist n. For Every real x. ~x=r -> d_n of r =/= d_n of x.
Of course all reals are to be represented by *INFINITE* binary decimal expansions, so 0.12 is represented as 0.120000...
So we are not speaking about the same distinguishability criterion.