Virgil
Posts:
8,833
Registered:
1/6/11


Re: The Distinguishability argument of the Reals.
Posted:
Jan 4, 2013 4:45 PM


In article <af7faea0149c4151966b1c656ab8ee6b@b11g2000yqh.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.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 > > > <3c1333396b4c4f74937f804bdaad3...@t5g2000vba.googlegroups.com>, > > > > > Zuhair <zaljo...@gmail.com> wrote: > > > > On Jan 4, 5:33 am, Virgil <vir...@ligriv.com> wrote: > > > > > In article > > > > > <6302ee90f0a24be59dbbc1f999c3a...@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 COUNTERINTUITIVENESS > > 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. 

