Virgil
Posts:
4,482
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 4, 2013 2:22 AM
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In article
<3c133339-6b4c-4f74-937f-804bdaad353e@t5g2000vba.googlegroups.com>,
Zuhair <zaljohar@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!
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