What is the continuum hypothesis?
Q: What is the continuum hypothesis?
A: The continuum hypothesis is a hypothesis that there is no set that is both bigger than that of the natural numbers and smaller than that of the real numbers.
Q: Who stated the continuum hypothesis and when?
A: Georg Cantor stated the continuum hypothesis in 1877.
Q: Are there infinitely many natural numbers?
A: Yes, there are infinitely many natural numbers.
Q: What is the cardinality of the set of natural numbers?
A: The cardinality of the set of natural numbers is infinite.
Q: Are there more real numbers than natural numbers?
A: Yes, there are more real numbers than natural numbers.
Q: Can the continuum hypothesis be falsified using Zermelo-Fraenkel set theory?
A: Kurt Gödel showed in 1939 that the hypothesis cannot be falsified using Zermelo-Fraenkel set theory.
Q: Who showed that the Zermelo-Fraenkel set theory cannot be used to prove the continuum hypothesis?
A: Paul Cohen showed in the 1960s that the Zermelo-Fraenkel set theory cannot be used to prove the continuum hypothesis.
