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> We encounter the paradox of P because of the definition.

The point of the problem is this: to create a program P that will tell us if f(x) halts or not. Q is simply a function that breaks P so that it cannot give the right answer. Thus making P impossible.

Paradoxes are irrelevant to the issue :)

(You're over thinking this a lot; read one of the formal proofs and it will address pretty much all of your points)




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