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From: olcott <polcott333@gmail.com>
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Subject: =?UTF-8?Q?A_simulating_halt_decider_applied_to_the_The_Peter_Linz_T?=
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On 5/26/2024 3:20 PM, Richard Damon wrote:
> On 5/26/24 3:14 PM, olcott wrote:
>> When Ĥ is applied to ⟨Ĥ⟩
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> When we see that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H in an
>> infinite number of steps cannot possibly reach its own simulated
>> final state of ⟨Ĥ.qn⟩ and halt then we correctly deduce that the
>> same thing applies when simulating halt decider embedded_H correctly
>> simulates less than an infinite number of steps of ⟨Ĥ⟩ ⟨Ĥ⟩.
>>
> 
> Nope.
> 
> Since we are talking about Turing Machines, your stipulated POOP 
> definitions go away, 

https://www.liarparadox.org/Linz_Proof.pdf
*Simplified the notation for Ĥ on the top of page three*
and put back in the qy state shown in figure 12.2

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

   Ĥ copies its own Turing machine description: ⟨Ĥ⟩
   then invokes embedded_H that simulates ⟨Ĥ⟩ with ⟨Ĥ⟩ as input.

It is an easily verified fact that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by 
embedded_H cannot possibly reach its own simulated final state of
⟨Ĥ.qn⟩ in any finite sequence of steps.

*If you want to lie about this or fail to understand this*
*irrefutable truth that only makes yourself look foolish*

Any academicians reading this post will further conclude
that your insults and ad hominem attacks are quite pathetic.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer