It has always been impossible to define an INPUT that does the opposite of its halt decider

On 6/9/2025 3:39 PM, Richard Heathfield wrote:

 On 09/06/2025 20:54, dbush wrote:

If you would just be honest about the fact that you're not working on the halting problem, people would stop bothering
you.

Well, I doubt if he'll ever do that, but we could stop bothering him anyway. You'd be amazed at how much time you save. :-)
 

I have refuted the halting problem proofs the
exact same way that ZFC refuted Russell's Paradox.
The halting problem proof crucially depends on defining
an *INPUT* that does the opposite of whatever value its
corresponding halt decider returns. It is not possible
to define such an *INPUT*.
int main()
{
   DDD(); // Is not an *INPUT* to the HHH(DDD)
}        // that this DDD calls.
When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
The computation that embedded_H is embedded within
is not an *INPUT* to embedded_H.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer