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Re: The Distinguishability argument of the Reals.
Posted:
Jan 4, 2013 6:41 AM
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On 4 Jan., 10:54, Zuhair <zaljo...@gmail.com> wrote:
> On Jan 4, 10:22 am, Virgil <vir...@ligriv.com> wrote:
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> > 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>,
>
> > > > 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.
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.
Regards, WM
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