query: Equality of Cardinality of a Power Set to a Set of Functions
positive_passages.docid: 145214
positive_passages.text: Showing the power set is equinumerous to ${}^X2$
negative_passages.docid: 37951
negative_passages.text: proof detail concerning bijection between a set and its power set
negative_passages.docid: 21431
negative_passages.text: The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
negative_passages.docid: 63148
negative_passages.text: Power Set Difference Proof P(A-B)=P(A)-P(B)
negative_passages.docid: 124060
negative_passages.text: Are these subsets of the powerset P(N) countable?
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: 52614
negative_passages.text: (exercise from Tao's analysis book) Proof of a lemma relating to power set of X
negative_passages.docid: 15733
negative_passages.text: Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$
negative_passages.docid: 29755
negative_passages.text: Power set equivalency of Axiom of Choice
negative_passages.docid: 63717
negative_passages.text: Is the closure of a set equal to the closure of the closure of that set?
negative_passages.docid: 98518
negative_passages.text: Cardinality of equivalence relations on N
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 62709
negative_passages.text: Functions that are sets of all function - proofs
negative_passages.docid: 125683
negative_passages.text: Power set of a finite set is finite proof, no cardinality of power set
negative_passages.docid: 23125
negative_passages.text: Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
negative_passages.docid: 41052
negative_passages.text: The set of real numbers and power set of the natural numbers
negative_passages.docid: 33064
negative_passages.text: Powerset of set with empty sets