Re: ZFC solution to incorrect questions: reject them

On 3/12/24 3:53 PM, olcott wrote:

On 3/12/2024 5:30 PM, Richard Damon wrote:

On 3/12/24 2:34 PM, olcott wrote:

On 3/12/2024 4:23 PM, Richard Damon wrote:

On 3/12/24 1:11 PM, olcott wrote:

On 3/12/2024 2:40 PM, Richard Damon wrote:

On 3/12/24 12:02 PM, olcott wrote:

On 3/12/2024 1:31 PM, immibis wrote:

On 12/03/24 19:12, olcott wrote:

∀ H ∈ Turing_Machine_Deciders
∃ TMD ∈ Turing_Machine_Descriptions  |
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
There is some input TMD to every H such that
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)

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And it can be a different TMD to each H.
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When we disallow decider/input pairs that are incorrect
questions where both YES and NO are the wrong answer

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Once we understand that either YES or NO is the right answer, the whole rebuttal is tossed out as invalid and incorrect.
>

>
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
BOTH YES AND NO ARE THE WRONG ANSWER FOR EVERY Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩

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No, because a given H will only go to one of the answers. THAT will be wrong, and the other one right.
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∀ H ∈ Turing_Machine_Deciders
∃ TMD ∈ Turing_Machine_Descriptions  |
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
Not exactly. A pair of otherwise identical machines that
(that are contained within the above specified set)
only differ by return value will both be wrong on the
same pathological input.

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You mean a pair of DIFFERENT machines. Any difference is different.

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Every decider/input pair (referenced in the above set) has a
corresponding decider/input pair that only differs by the return
value of its decider.

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Nope.
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∀ H ∈ Turing_Machines_Returning_Boolean
∃ TMD ∈ Turing_Machine_Descriptions  |
Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
 Every H/TMD pair (referenced in the above set) has a
corresponding H/TMD pair that only differs by the return
value of its Boolean_TM.

That isn't in the set above.

 That both of these H/TMD pairs get the wrong answer proves that
their question was incorrect because the opposite answer to the
same question is also proven to be incorrect.
 

Nope, since both aren't in the set selected.
You just don't understand what that statement is saying.
I've expalined it, but it seems over you head.
For Every H, we show we can find at least one input (chosen just for that machine) that it will get wrong.
Thus, no H computes the Halting Property.
Never will two machine that give opposite results be given the exact same input, and your claiming that just shows you are a stupid pathological liar.
They CAN'T be as the two will give opposite Predicted Behaviors, and thus one will be correct, so that input won't be selected for that machine.
In fact, the proven TMD to give to each machine is based on the Decider it will be given to, and the opposite outputs will generate different "pathological inputs" so you claim just won't happen.
You are just proving your stupidity.