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From: immibis <news@immibis.com>
Newsgroups: comp.theory
Subject: Re: D correctly simulated by H cannot possibly halt --- templates and
 infinite sets
Date: Thu, 30 May 2024 19:58:12 +0200
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In-Reply-To: <v39ttg$1mtd9$1@dont-email.me>

On 30/05/24 15:11, olcott wrote:
> On 5/30/2024 4:11 AM, joes wrote:
>> Am Wed, 29 May 2024 22:48:45 -0500 schrieb olcott:
>>> *A deciders compute the mapping*
>>> FROM ITS INPUTS
>>> *to it own accept or reject state*
>>>
>>> *Deciders cannot take*
>>> ACTUAL TURING MACHINES AS INPUTS
>>>
>>> *Deciders can only take*
>>> FINITE STRINGS AS INPUTS
>> Poetic.
>> What is an „actual Turing machine”?
>>
> 
> *Formalizing the Linz Proof structure*
> ∃H  ∈ Turing_Machines
> ∀x  ∈ Turing_Machine_Descriptions
> ∀y  ∈ Finite_Strings
> such that H(x,y) = Halts(x,y)
> 
> Every H is an actual Turing_Machine
> 
> Every x is a Turing_Machine_Description
> thus not an actual Turing_Machine
> 
> 

∃H  ∈ Turing_Machines
∀x  ∈ Turing_Machines
∀y  ∈ Finite_Strings
such that H(DescriptionOf(x),y) = Halts(x,y)