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Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 26, 2012 10:30 AM
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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.
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 oterhbut for at least some infinite
> set, no finite set of finite initial segments suffices.
And no infinite set is available. Therefore even the Cantor list must
be infinite. But without finite definition, the Cantor-list is as
undefined as its diagonal.
>
> What drives WM is shear orneryness.
What is that? In doubt I contradict.
Regards, WM
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