query: How do I prove that there doesn't exist a set whose power set is countable?
positive_passages.docid: 42095
positive_passages.text: Existence in ZF of a set with countable power set
negative_passages.docid: 158882
negative_passages.text: Prove the existence of some weird family of sets
negative_passages.docid: 35043
negative_passages.text: Cardinality of a set A is strictly less than the cardinality of the power set of A
negative_passages.docid: 52682
negative_passages.text: Is the power set of the natural numbers countable?
negative_passages.docid: 157513
negative_passages.text: How can I prove that these sets are countable infinite?
negative_passages.docid: 144735
negative_passages.text: Possible cardinality of power sets
negative_passages.docid: 60678
negative_passages.text: Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
negative_passages.docid: 110957
negative_passages.text: No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
negative_passages.docid: 114770
negative_passages.text: Proof that a perfect set is uncountable
negative_passages.docid: 76240
negative_passages.text: How is $\epsilon_0$ countable?
negative_passages.docid: 71922
negative_passages.text: Prove Uncountable set minus a countable set is uncountable
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 88904
negative_passages.text: Help with a proof. Countable sets.
negative_passages.docid: 125411
negative_passages.text: Infinite set always has a countably infinite subset
negative_passages.docid: 99478
negative_passages.text: countably infinite union of countably infinite sets is countable
negative_passages.docid: 111723
negative_passages.text: Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
negative_passages.docid: 25834
negative_passages.text: Proof a set cannot contain its own powerset - Russell's Paradox