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Among Gödel's contributions, what did he prove regarding the accepted Zermelo–Fraenkel set theory?
That its axioms are inconsistent
That neither the axiom of choice nor the continuum hypothesis can be disproved from its axioms
That it is a complete system
That it contradicts quantum mechanics
Answer
Gödel proved that neither the axiom of choice nor the continuum hypothesis can be disproved from the axioms of Zermelo–Fraenkel set theory. This means that they are independent of the other axioms, and cannot be proved or disproved using them. This is a significant result, as it shows that there are limits to what can be proven in mathematics.
The Gödelicious Quiz: Unraveling the Genius of Kurt Gödel
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