Date: Jan 4, 2013 1:08 AM
Author: Zaljohar@gmail.com
Subject: Re: The Distinguishability argument of the Reals.

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