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From: Mikko <mikko.levanto@iki.fi>
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Subject: =?utf-8?Q?Re:_A_simulating_halt_decider_applied_to_the_The_Peter_Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9_--_key_details?=
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On 2024-06-02 13:07:25 +0000, olcott said:

> On 6/2/2024 2:36 AM, Mikko wrote:
>> On 2024-06-01 14:37:01 +0000, olcott said:
>> 
>>> On 6/1/2024 2:52 AM, Mikko wrote:
>>>> On 2024-05-31 15:35:18 +0000, olcott said:
>>> 
>>>>> 
>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>> 
>>>> Of those two lines one is false.
>>>> As embedded_H is a copy of H both lines imply that H is not a halt decider.
>>>> 
>>>>> *Formalizing the Linz Proof structure*
>>>>> ∃H  ∈ Turing_Machines
>>>>> ∀x  ∈ Turing_Machine_Descriptions
>>>>> ∀y  ∈ Finite_Strings
>>>>> such that H(x,y) = Halts(x,y)
>>>> 
>>>> As already noted, the above is not a part of a proof structure.
>>>> 
>>> 
>>> Unless and until you provide reasoning to back that up it counts
>>> as if you said nothing about it.
>> 
>> If there are no more questions about the details of the reasoning
>> we may assume that the presiented reasoning is sufficieant.
>> 
> 
> The above <is> the structure of his proof your empty assertion utterly 
> bereft of any supporting (EAUBoaSR)) reasoning counts for zilch.

Those how know what "structure" means can see that it is not a structure.

> Linz claims that of every Turing Machine there are none that solve the 
> halting problem.

And proves the claim.

> ∃!H  ∈ Turing_Machines  (What Richard was saying)
> would say that there does not exist exactly one Turing Machine that
> solves the halting problem thus fails if there are more than one.

Irrelevant as that is not what Linz' says.
And you should not lie about Rchard.

-- 
Mikko