Talk:Turing's proof
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Problems with the first proof:
Suppose I switch D with a simple machine that always outputs "s". In such a case, H would loop when reaching K anyway. Doesn't it kind of makes the H machine fail by itself, making the need of D for it to fail irrelevant? And wouldn't it invalidate the proof about the existence of D? I don't mean to say that the Halting Problem isn't undecidable, but just that Turing's original proof is flawed. Or am I missing an important point here?
I've got it! The point is that D cannot output correctly its analysis of H. If D decides that H is circle-free, H becomes circular. And if D decides that H is circular, H becomes circle-free, since it wouldn't have to enter that whole circular calculation of itself. Therefore, D cannot be always right!
Summary of the Third Proof
[edit]Was written "Here Turing proves "that the Hilbert Entscheidungsproblem can have no solution" (Undecidable, p. 145). Here"
The definition of the word "can" is useful. It means is able to or permitted to. — Preceding unsigned comment added by 174.250.64.202 (talk) 21:46, 14 March 2021 (UTC)
At least change the title
[edit]I'm not sure this proof belongs on Wikipedia, or in a separate article; if it does, then that article must have a title and intro that make some sense to non-experts. Rp (talk) 11:57, 24 March 2024 (UTC)