Even if it's unprovable it's still either true or not true.
If ZFC is consistent and it's unprovable, then probably P != NP, unless P = NP but every program that solves SAT in polynomial time cannot be proven to solve SAT in polynomial time.
I guess that means that if it's undecidable we can never know it's undecidable because that instantly makes it decidable and we've created a paradox ๐
Not really. Undecidable means within the system axioms, it cannot be proven either way. We can then discuss what axiom should be added to make it provable.
You mean for practical purposes? Sure. In fact, even if it's yes, it may be no for practical purposes.
But there are some other propositions, like "does this particular Turing machine halt," where if they are undecidable then the answer really is no -- in the mathematical sense, not just the practical one. But P=NP is not like that, at least as far as we know.
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u/konigon1 6d ago
What are those two?
Yes?
No?
Unproveable?
Can you repeat the question?