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Topic: Matheology sqrt(-2): WM admits to unlistability of 0/1 sequences
Replies: 76   Last Post: Dec 28, 2013 7:39 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology sqrt(-2): WM admits to unlistability of 0/1 sequences
Posted: Dec 20, 2013 11:14 AM

On Friday, 20 December 2013 15:56:54 UTC+1, wpih...@gmail.com wrote:
> To be precise:
>
>
>
> There is no potentially infinite list of potentially infinite 0/1
>
> sequences, L, with the property that any potentially infinite 0/1 sequence
>
> is in L

Correct. In my example with the rationals-complete list I assume actual infinity. But even in this branch of matheology there is no antidiagonal with more digits than all d_n, n in |N.

And if d never differs from all rationals, then there are rationals which parallel d up to every digit. Numbers which are parallel (identical) up to every digit are identical numbers.

In fact, however, numbers are not given by digits but by a finite formula. That means d, defined by a finite formula, differs in fact from all rational numbers of the list. But that cannot be shwon by digits.

And the number of finite formulas is countable.

Regards, WM

Date Subject Author
12/20/13 William Hughes
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