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On 10/03/24 19:32, olcott wrote:Not in the case of Russell's Paradox.On 3/10/2024 1:08 PM, immibis wrote:all decision problems are defined so that all instances are valid or else they are not defined properlyOn 10/03/24 18:17, olcott wrote:>ZFC simply tossed out the Russell's Paradox question as unsound.>
So you are saying that some Turing machines are not sound?
>>ZFC simply tossed out the Russell's Paradox question as unsoundBoth H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decide that:>
(a) Their input halts H.qy
(b) Their input fails to halt or has a pathological
relationship to itself H.qn.
But the "Pathological Relationship" is ALLOWED.
>
expressly disallowing the "Pathological Relationship".
So you are saying that some Turing machines are not real Turing machines?
>I am only claiming that both H and Ĥ.H correctly say YES>
when their input halts and correctly say NOT YES otherwise.
well the halting problem requires them to correctly say NO, so you haven't solved it
All decision problem instances of program/input such that both
yes and no are the wrong answer toss out the input as invalid.
>
all turing machine/input pairs are valid instances of the halting problem--
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