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


Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 26, 2012 3:26 PM


In article <d7e06e32533c4b90a1a6c51cc211c311@a6g2000vbh.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 26 Dez., 10:21, Virgil <vir...@ligriv.com> wrote: > > > Note, however, that there is no finite initial segment of any one > > infinite binary sequence that distinguishes it from ALL others. > > Note that there is no sequence of digits that alone defines a number.
Actually there are lots of finite sequences of digits that define numbers quite effectively,
> You need always a finite definition like 0.111 and so in infinity. > > You cannot use a finite sequence of digits alone to define a number, > because something unexpected could follow. And you cannot an infinite > sequence of digits to define a number, because the definition would > never get ready. All you can do is to use a finite definition like 1/3 > or 0.111... or 0.25 and the rest is silence or zeros. > > > > For any finite set of such strings, finite initial segments suffice to > > distinguish all of them from each other but for at least some infinite > > set, no finite set of finite initial segments suffices. > > And no infinite set is available.
At least not in WMytheology. > Therefore even the Cantor list must > be infinite.
> But without finite definition, the Cantorlist is as > undefined as its diagonal.
It is those who claim that the set of digit strings is countable who must create that allegedly impossible listing to prove that that set satisfies the definition of countability.
Any set whose members cannot be 'listed' is, by definition, uncountable.
If WM chooses to say that the set of real numbers, or the set of endless binary strings cannot be listed, then it is WM who is arguing that those sets are uncountable. > > > > What drives WM is shear orneryness. > > What is that? The necessary quality for membership in your WMytheology. 

