Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets

On 5/30/2024 4:11 AM, joes wrote:

Am Wed, 29 May 2024 22:48:45 -0500 schrieb olcott:

On 5/29/2024 9:55 PM, Richard Damon wrote:

On 5/29/24 10:36 PM, olcott wrote:

On 5/29/2024 9:25 PM, Richard Damon wrote:

On 5/29/24 9:55 PM, olcott wrote:

When the category is examined all at once then there is no need
to look at each individual element.

So, which one or ones gave the correct answer for their input?

 

*Formalizing the Linz Proof structure*
∃H  ∈ Turing_Machines
∀x  ∈ *Turing_Machines_Descriptions*
∀y  ∈ Finite_Strings
such that H(x,y) = Halts(x,y)
>
When we formalize it that way then some simulating halt deciders
get the correct answer.
>
*Everyone else implicitly assumes this incorrect formalization*
∃H  ∈ Turing_Machines
∀x  ∈ *Turing_Machines*
∀y  ∈ Finite_Strings
such that H(x,y) = Halts(x,y)
>

Nope.
You just don't understand the meaning of a "Description" in the problem.
>

I have an OCD/Aspergers degree of single-minded focus.

Checks out.
 

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