query: Subset of an uncountable set
positive_passages.docid: 28539
positive_passages.text: Does any uncountable set contain two disjoint uncountable sets?
negative_passages.docid: 9850
negative_passages.text: How many ways are there to choose 3 subsets $A,B,C$ of a set $\{1,2,3...n\}$ such that $ A \cap B \cap C = \emptyset $
negative_passages.docid: 68230
negative_passages.text: The cardinality of a countable union of sets with less than continuum cardinality
negative_passages.docid: 80180
negative_passages.text: Discrete and compact subset must be finite
negative_passages.docid: 2403
negative_passages.text: Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
negative_passages.docid: 9021
negative_passages.text: An infinite subset of a countable set is countable
negative_passages.docid: 140799
negative_passages.text: Prove that there exist uncountable family of subsets of $\mathbb{N}$ which is linearly (totally) ordered by relation of inclusion.
negative_passages.docid: 114770
negative_passages.text: Proof that a perfect set is uncountable
negative_passages.docid: 153072
negative_passages.text: Guessing a subset of $\{1,...,N\}$
negative_passages.docid: 132537
negative_passages.text: Class of sets of a given infinite cardinality
negative_passages.docid: 63678
negative_passages.text: Let $A$ and $B$ be countable sets. Is there any function $f$ such that a certain condition holds for an uncountable number of functions $g$?
negative_passages.docid: 116676
negative_passages.text: Examples of uncountable sets with zero Lebesgue measure
negative_passages.docid: 95747
negative_passages.text: Number of countable subsets of $\mathbb{R}$
negative_passages.docid: 156335
negative_passages.text: Proving Power Set of $\mathbb N$ is Uncountable
negative_passages.docid: 324
negative_passages.text: Show uncountable set of real numbers has a point of accumulation
negative_passages.docid: 97697
negative_passages.text: Countable union of sets of cardinality $c$ has cardinality $c$
negative_passages.docid: 107614
negative_passages.text: Partitioning an infinite set