```Date: Jan 4, 2013 4:54 AM
Author: Zaljohar@gmail.com
Subject: Re: The Distinguishability argument of the Reals.

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 thinkthat the argument that I've presented shows some COUNTER-INTUITIVENESSto uncountability, that's all.Zuhair
```