query: Cardinality of set and its power set
positive_passages.docid: 35043
positive_passages.text: Cardinality of a set A is strictly less than the cardinality of the power set of A
negative_passages.docid: 86421
negative_passages.text: Proof of the definition of cardinal exponentiation
negative_passages.docid: 29755
negative_passages.text: Power set equivalency of Axiom of Choice
negative_passages.docid: 126015
negative_passages.text: Elementary number theory in sets
negative_passages.docid: 142886
negative_passages.text: Find set with maximal cardinality given constraints
negative_passages.docid: 21663
negative_passages.text: Bijection between power sets of sets implies bijection between sets?
negative_passages.docid: 9651
negative_passages.text: Cardinality of cartesian product of an infinite set with N
negative_passages.docid: 48523
negative_passages.text: Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
negative_passages.docid: 44214
negative_passages.text: The number of subsets of a set of cardinality $n$
negative_passages.docid: 89712
negative_passages.text: For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
negative_passages.docid: 12436
negative_passages.text: The cardinality of the set of all finite subsets of an infinite set
negative_passages.docid: 60216
negative_passages.text: Power Set Explanation
negative_passages.docid: 7785
negative_passages.text: Cardinality of sum-set
negative_passages.docid: 83518
negative_passages.text: Proving Two sets have same cardinality
negative_passages.docid: 124060
negative_passages.text: Are these subsets of the powerset P(N) countable?
negative_passages.docid: 122947
negative_passages.text: What is the cardinality of the set of infinite cardinalities?
negative_passages.docid: 109054
negative_passages.text: Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?