On Jan 4, 10:22 am, Virgil <vir...@ligriv.com> wrote: > In article > <3c133339-6b4c-4f74-937f-804bdaad3...@t5g2000vba.googlegroups.com>, > > > > > > > > > > Zuhair <zaljo...@gmail.com> wrote: > > 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. > > > Zuhair > > Exactly! > --
which mean that your objection is irrelevant to my argument. I think that the argument that I've presented shows some COUNTER-INTUITIVENESS to uncountability, that's all.