But if it’s true that there doesn’t exist a proof that it halts, then it will run forever searching for one.
No; provable and true are not the same thing. It may be the case that the program halts, but it is nevertheless impossible to prove that it halts except by “run it and see”, which doesn’t count.
No; provable and true are not the same thing. It may be the case that the program halts, but it is nevertheless impossible to prove that it halts except by “run it and see”, which doesn’t count.