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

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.
20 years ago I tested 50% above normal on the Aspergers test.
Because I have focused this concentration of having empathy
I now score 50% below normal on Asperger tests.
The issue is that everyone else has not paid close enough
attention to what a decider does.
*A deciders compute the mapping*
FROM ITS INPUTS
FROM ITS INPUTS
FROM ITS INPUTS
FROM ITS INPUTS
FROM ITS INPUTS
*to it own accept or reject state*
*Deciders cannot take*
ACTUAL TURING MACHINES AS INPUTS
ACTUAL TURING MACHINES AS INPUTS
ACTUAL TURING MACHINES AS INPUTS
ACTUAL TURING MACHINES AS INPUTS
ACTUAL TURING MACHINES AS INPUTS
*Deciders can only take*
FINITE STRINGS AS INPUTS
FINITE STRINGS AS INPUTS
FINITE STRINGS AS INPUTS
FINITE STRINGS AS INPUTS
FINITE STRINGS AS INPUTS
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer