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?

Brent
--
    Oh, BTW, Bruno wrote the above ... not me.

--
Onward!

Stephen

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