```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 thelongest 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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