On 11/1/2012 1:19 AM, meekerdb wrote:

On 10/31/2012 6:58 PM, Stephen P. King wrote:

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`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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