Catch and then what? Return to what?
kogasa
joined 1 year ago
Just explaining that the limitations of Gödel's theorems are mostly formal in nature. If they are applicable, the more likely case of incompleteness (as opposed to inconsistency) is not really a problem.
Dunno what you're trying to say. Yes, if ZFC is inconsistent it would be an issue, but in the unlikely event this is discovered, it would be overwhelmingly probable that a similar set of axioms could be used in a way which is transparent to the vast majority of mathematics. Incompleteness is more likely and less of an issue.
It's extremely unlikely given the pathological nature of all known unprovable statements. And those are useless, even to mathematicians.
Nobody is practically concerned with the "incompleteness" aspect of Gödel's theorems. The unprovable statements are so pathological/contrived that it doesn't appear to suggest any practical statement might be unprovable. Consistency is obviously more important. Sufficiently weak systems may also not be limited by the incompleteness theorems, i.e. they can be proved both complete and consistent.
That's the "naughty" guy from Courage the Cowardly Dog
It would be, since assembly is written for a machine that already exists. In Minecraft you have to build the machine and create your own assembly first. It doesn't have to be a complex architecture though.
Yes. A matrix is unitary if the conjugate transpose (conjugate as in "complex conjugate") is equal to its inverse.
Still not enough, or at least pi is not known to have this property. You need the number to be "normal" (or a slightly weaker property) which turns out to be hard to prove about most numbers.
It sounds like you don't understand the complexity of the game. Despite being finite, the number of possible games is extremely large.
These things are specifically not defined by the protocol. They could be. They're not, by design.
Sure, throw people in jail who haven't committed a crime, that'll fix all kinds of systemic issues