Re: How the requirements that Professor Sipser agreed to are exactly met

On 5/13/2025 12:11 AM, Richard Heathfield wrote:

On 13/05/2025 03:01, olcott wrote:

If the Goldbach conjecture is true (and there is
no short-cut)

 We don't know that. Fermat's Last Theorem had a short cut, but it took 358 years to find it. At that rate, we won't find Goldbach's short cut (if it has one) for another 75 years.
 

this requires testing against every
element of the set of natural numbers an infinite
computation.

 Only if it's true. So if it's true, the testing program will never halt. But if it's false, the tester will eventually find the counter-example, print it, and stop.
 So a program that can tell whether another program will halt can tell us whether Goldbach's conjecture is true.
 It would be the short cut that you say doesn't exist.
 

I am refuting the key halting problem, proof
I am not refuting the halting problem.
As soon as it is understood that I am correct
that HHH(DD) computes the mapping from its
input to recursive emulation. Then in a few small
steps it will be know that I refuted the conventional
Halting Problem proofs.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer