Virgil
Posts:
4,483
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 4, 2013 4:45 PM
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In article
<af7faea0-149c-4151-966b-1c656ab8ee6b@b11g2000yqh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 4 Jan., 10:54, Zuhair <zaljo...@gmail.com> wrote:
> > 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.
>
> Those are not different numbers. Such objects cannot appear in any
> Cantor list as entries or diagonal
>
> > > > Of course all reals are to be represented by *INFINITE* binary decimal
> > > > expansions, so 0.12 is represented as 0.120000...
>
> It is impossible to represent any real number by an infinite expansion
> that is not defined by a finite word.
> >
> > > > So we are not speaking about the same distinguishability criterion.
>
> There is no other criterion.
> >
> > which mean that your objection is irrelevant to my argument. I think
> > that the argument that I've presented
>
> that you have parroted without understanding its implications
>
> > shows some COUNTER-INTUITIVENESS
> > to uncountability, that's all.
>
> Have you ever seen that Cantor's argument works without
> distinguishability? Why must b_n =/= a_nn? Never wondered why that is
> required at a finite n?Anybody who pretends that there are numbers
> that cannot be distinguished is outside of mathematics and even
> outside of Cantor's argument and its implications.
And until WM can produce a surjection from N to R, none of his claims
that the reals are countable show that the definition of countability
for R can be met.
Thus R remains uncounted even in Wolkenmuekenheim.
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