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>,
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>  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>,

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> > > Zuhair <zaljo...@gmail.com> wrote:
> > > > Since all reals are distinguished by finite initial
> > > > segments of them,

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> > > Some reals are distinguished by finite initial segments of their decimal
> > > representations, most are not.

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> > r is distinguishable on finite basis iff For Every real x. ~x=r ->
> > Exist n: d_n of r =/= d_n of x.

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> > As far as I know every real is so distinguishable.
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> > In your version you changed the quantifier order, your version is
> > speaking about the following:

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> > r is distinguishable on finite basis iff Exist n. For Every real x.
> > ~x=r -> d_n of r =/= d_n of x.

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> > Of course all reals are to be represented by *INFINITE* binary decimal
> > expansions, so 0.12 is represented as 0.120000...

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> > So we are not speaking about the same distinguishability criterion.
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> > 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.

Zuhair