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Topic: Matheology § 257
Replies: 11   Last Post: Apr 23, 2013 5:05 PM

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Scott Berg

Posts: 2,037
Registered: 12/12/04
Re: Matheology � 257
Posted: Apr 22, 2013 2:17 PM
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"WM" <> wrote in message

Matheology § 257

>The set of all possible computer programs is countable {{if going into
>concrete details of computers, we can even say more restrictively: The
>number of all possible programs is finite and certainly less than

that is not proof, you are simply guessing.

>But of course Turing did not refer to real computers and did
>not know anything about the memory space of an exploitable
>surronding. Therefore let us analyze his approach here.}}, therefore
>the set of all computable reals is countable, and diagonalizing over
>the computable reals immediately yields an uncomputable real. Q.E.D.
>{{Well, it is not always that easy to diagonalize over finite
>sequences. The following list has no diagonal:
>So we must take some more care, as will be done in the following.}}
> Let's do it again more carefully.
> Make a list of all possible computer programs. Order the programs
>by their size, and within those of the same size, order them
>alphabetically. The easiest thing to do is to include all the possible
>character strings that can be formed from the finite alphabet of the
>programming language, even though most of these will be syntactically
>invalid programs.

so now you are *not* using computer programs.....
a sequence from some finite alphabet,
why not just a binary string
(representing (not), wait for it, *psudo machine code*! )

> Here's how we define the uncomputable diagonal number 0 < r < 1.
>Consider the kth program in our list. If it is syntactically invalid,
>or if the kth program never outputs a kth digit, or if the kth digit
>output by the kth program isn't a 3, pick 3 as the kth digit of r.
>Otherwise, if the kth digit output by the kth program is a 3, pick 4
>as the kth digit of r.

why 3 or 4 ? who is picking ? There Nose ?

>. After all you cannot use a program that is longer than the
longest program that is used.

depends on when it is used, then it can add a byte to make itself longer
after you have used it.

>Regards, WM

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