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On 3/12/24 12:02 PM, olcott wrote:∀ H ∈ Turing_Machine_DecidersOn 3/12/2024 1:31 PM, immibis wrote:No, because a given H will only go to one of the answers. THAT will be wrong, and the other one right.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)
And it can be a different TMD to each H.
>When we disallow decider/input pairs that are incorrect>
questions where both YES and NO are the wrong answer
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⟩
Remember, you above statement was built on the ASSUMPTION that a correct H existed, and thus the contradiction you see just says that no such H exists, not that the original question was incorrect.--
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