Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: The Distinguishability argument of the Reals.
Posted: Jan 4, 2013 4:45 PM

In article
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

> >
> > >  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.
--

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