Date: Apr 22, 2013 2:17 PM
Author: Scott Berg
Subject: Re: Matheology � 257

"WM" <mueckenh@rz.fh-augsburg.de> wrote in message

news:800fc644-1b3d-4161-930b-9844d1826854@cd3g2000vbb.googlegroups.com...

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

>2^10^100.

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:

>0

>1

>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