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Topic: The Distinguishability argument of the Reals.
Replies: 83   Last Post: Jan 7, 2013 12:58 AM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: The Distinguishability argument of the Reals.
Posted: Jan 4, 2013 6:41 AM

On 4 Jan., 10:54, Zuhair <zaljo...@gmail.com> wrote:
> On Jan 4, 10:22 am, Virgil <vir...@ligriv.com> wrote:
>
>
>
>
>

> > In article

>
> >  Zuhair <zaljo...@gmail.com> wrote:
> > > On Jan 4, 5:33 am, Virgil <vir...@ligriv.com> wrote:
> > > > In article

>
> > > > 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.

Regards, WM

Date Subject Author
1/1/13 Zaljohar@gmail.com
1/2/13 mueckenh@rz.fh-augsburg.de
1/2/13 Virgil
1/3/13 Virgil
1/3/13 Zaljohar@gmail.com
1/3/13 gus gassmann
1/3/13 Zaljohar@gmail.com
1/3/13 gus gassmann
1/3/13 Zaljohar@gmail.com
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 fom
1/4/13 Zaljohar@gmail.com
1/4/13 fom
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 fom
1/3/13 Virgil
1/4/13 gus gassmann
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/4/13 Virgil
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/4/13 Virgil
1/4/13 gus gassmann
1/4/13 ross.finlayson@gmail.com
1/5/13 Virgil
1/5/13 ross.finlayson@gmail.com
1/5/13 Virgil
1/5/13 fom
1/5/13 ross.finlayson@gmail.com
1/6/13 fom
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/7/13 ross.finlayson@gmail.com
1/7/13 Virgil
1/3/13 fom
1/3/13 fom
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/6/13 Virgil
1/6/13 fom
1/6/13 Virgil
1/6/13 fom
1/6/13 ross.finlayson@gmail.com
1/4/13 Virgil
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 forbisgaryg@gmail.com
1/3/13 Virgil
1/4/13 Zaljohar@gmail.com
1/4/13 Virgil
1/4/13 Zaljohar@gmail.com
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/5/13 Virgil
1/4/13 Virgil
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/4/13 Virgil
1/2/13 Bill Taylor