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

On 5/30/24 9:11 AM, olcott wrote:

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
 

But represents one, and thus we can determine the actual behavior of that Turing Machine so desceribed.
And, if you actually READ what Linz says, his formalation would be:
For Halting to be computable we must have:
∃H  ∈ Turing_Machines such that
∀M  ∈ Turing_Machines, with a description Wm, and
∀w  ∈ Finite_Strings
such that H(Wm,w) = Halts(M,w)
Try to read his work a bit betetr.
He describes FIRST having a Turing Machine M to be decided on, and THEN converts it to Wm to give it to the decider.
SKippig steps is not allowed.