query: Is there a powerset with the cardinality of the natural numbers?
positive_passages.docid: 42095
positive_passages.text: Existence in ZF of a set with countable power set
negative_passages.docid: 73850
negative_passages.text: Cardinality of set of functions
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 36612
negative_passages.text: Strange set notation (a set as a power of 2)?
negative_passages.docid: 48535
negative_passages.text: Obtaining a powerset of a set in Java
negative_passages.docid: 126015
negative_passages.text: Elementary number theory in sets
negative_passages.docid: 106325
negative_passages.text: Question about Cardinality
negative_passages.docid: 136069
negative_passages.text: Is there a simple formula for the cardinality of $\{A\subseteq\kappa\mid |A|\leq\lambda\}$ when $\lambda\leq\kappa$?
negative_passages.docid: 83518
negative_passages.text: Proving Two sets have same cardinality
negative_passages.docid: 1396
negative_passages.text: cardinality of all real sequences
negative_passages.docid: 47697
negative_passages.text: Russell's paradox: a set cannot contain its own powerset
negative_passages.docid: 3217
negative_passages.text: Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers
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: 116501
negative_passages.text: How to show equinumerosity of  the powerset of $A$ and the set of functions from $A$ to $\{0,1\}$ without cardinal arithmetic?
negative_passages.docid: 79974
negative_passages.text: The cardinality of Lebesgue sets
negative_passages.docid: 121366
negative_passages.text: Intervals and cardinality
negative_passages.docid: 98850
negative_passages.text: A positional number system for enumerating fixed-size subsets?