query: Union of disjoint countable sets is countable
positive_passages.docid: 18223
positive_passages.text: Prove that the union of two disjoint countable sets is countable
negative_passages.docid: 114990
negative_passages.text: Is the complement of countably many disjoint closed disks path connected?
negative_passages.docid: 136006
negative_passages.text: Prove that any countable cartesian product of countable sets is countable
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 84936
negative_passages.text: The set of all finite sequences of members of a countable set is also countable
negative_passages.docid: 143586
negative_passages.text: Is $[0,1]$ a union of family of disjoint closed intervals?
negative_passages.docid: 23442
negative_passages.text: Cardinality of the union of infinite and countable sets
negative_passages.docid: 50880
negative_passages.text: Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
negative_passages.docid: 147136
negative_passages.text: Subset of a countable set is itself countable
negative_passages.docid: 28539
negative_passages.text: Does any uncountable set contain two disjoint uncountable sets?
negative_passages.docid: 136094
negative_passages.text: $G_\delta$ singletons in compact Hausdorff and first countability
negative_passages.docid: 108957
negative_passages.text: Cardinality of a totally ordered union
negative_passages.docid: 154474
negative_passages.text: Image of countable and uncountable sets
negative_passages.docid: 40937
negative_passages.text: Is the set of partial order relations over $ \mathbb{N}$ countable?
negative_passages.docid: 64871
negative_passages.text: Closure of Union contains Union of Closures
negative_passages.docid: 94825
negative_passages.text: Open set as a finite union of closed sets
negative_passages.docid: 4111
negative_passages.text: Outer measure is countably subadditive