On 11/1/2012 1:19 AM, meekerdb wrote:
On 10/31/2012 6:58 PM, Stephen P. King wrote:
Enumerate the programs computing functions fro N to N, (or the
equivalent notion according to your chosen system). let us call those
functions: phi_0, phi_1, phi_2, ... (the phi_i)
Let B be a fixed bijection from N x N to N. So B(x,y) is a number.
The number u is universal if phi_u(B(x,y)) = phi_x(y). And the
equality means really that either both phi_u(B(x,y)) and phi_x(y) are
defined (number) and that they are equal, OR they are both undefined.
In phi_u(B(x,y)) = phi_x(y), x is called the program, and y the data.
u is the computer. u i said to emulate the program (machine, ...) x
on the input y.
So u could be any number, depending on how you enumerated the
functions and what bijection is used?
Oh, BTW, Bruno wrote the above ... not me.
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