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.