Re: Halting Problem Proof ERROR

On 7/19/2025 12:23 PM, Richard Damon wrote:

On 7/19/25 10:23 AM, olcott wrote:>>

When you change my words and use those words as the basis
of your rebuttal you know that you cheat.
>
The infinite simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H
cannot possibly reach its own simulated final
halt state of ⟨Ĥ.qn⟩ you fucking moron.

 Which is just a strawman, as the definition of non-halting behavior of the input, is that when the machine the input describes,

If you only learn by rote memorization it may seem that way.
When you have a depth of understanding then you see that
what you said is merely an incorrect paraphrase of this:
Turing machine (at least partial) halt deciders only compute
the mapping from their finite string inputs to the actual
behavior that this input finite string actually specifies.
Conventional notation of a Turing Machine: Ĥ
Conventional notation of a TM description: ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞,
   if Ĥ applied to ⟨Ĥ⟩ halts, and
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
   if Ĥ applied to ⟨Ĥ⟩ does not halt.
*Is corrected to this*
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞
     ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H reaches
     its simulated final halt state of ⟨Ĥ.qn⟩, and
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
     ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H cannot possibly
     reach its simulated final halt state of ⟨Ĥ.qn⟩.
*Original proof*
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer