Re: Incorrect questions and halt deciders

On 3/14/24 12:24 PM, olcott wrote:

On 3/14/2024 11:40 AM, immibis wrote:

On 14/03/24 06:07, olcott wrote:

On 3/13/2024 11:58 PM, immibis wrote:

On 14/03/24 05:31, olcott wrote:

On 3/13/2024 11:22 PM, immibis wrote:

On 14/03/24 04:19, olcott wrote:

I did not say that precisely enough.
There is no mapping from the specific TM/input pair:
H(D,D) to Halts(D,D)

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Be even more precise because this doesn't seem to mean anything.

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*The same question exists in a hierarchy of generality to specificity*
There is a mapping from    D(D) to Halts(D,D).
There is a mapping from H1(D,D) to Halts(D,D)
There is no mapping from H(D,D) to Halts(D,D)
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>

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What is a mapping from D(D) to Halts(D,D)? What do those words mean?

Halts(D,D) is a standard hypothetical function used to denote the the halting behavior that D(D) actually has. It is a notational convention.
>
mapping from D(D) to Halts(D,D)
maps the actual behavior of D(D) to its actual halt status.
mapping from H1(D,D) to Halts(D,D)==1 meaning that D(D) halts.

>
You still did not explain what you mean by a mapping from D(D) to Halts(D,D). You only explained what you mean by Halts(D,D).

 Halts(D,D) is stipulated to correspond to the actual behavior of D(D)
map(H1(D,D),Halts(D,D))==true
map(H(D,D),Halts(D,D))==false
 Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn     // Ĥ applied to ⟨Ĥ⟩ does not halt
∀Ĥ.H (Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ != Halts(⟨Ĥ⟩, ⟨Ĥ⟩))
 

In other words, you don't know what a MAPPING means, proving your stupiditiy and ignorance.