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
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