query: Countable Union of sets of the same cardinality
positive_passages.docid: 151295
positive_passages.text: Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
negative_passages.docid: 66398
negative_passages.text: Union of a finite set and a countably infinite set is countably infinite
negative_passages.docid: 32081
negative_passages.text: The dual version of trichotomy of cardinality without AC
negative_passages.docid: 24685
negative_passages.text: Expressing a Countable Union of Sets as the Countable Union of Disjoint Sets (e.g. Eliminating Duplicate Intersections)
negative_passages.docid: 120562
negative_passages.text: If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality
negative_passages.docid: 3636
negative_passages.text: Are any two uncountable sets similar to each other?
negative_passages.docid: 14972
negative_passages.text: Cardinality of Vitali sets: countably or uncountably infinite?
negative_passages.docid: 122506
negative_passages.text: Relation on countable sets
negative_passages.docid: 9082
negative_passages.text: Do sets, whose power sets have the same cardinality, have the same cardinality?
negative_passages.docid: 99478
negative_passages.text: countably infinite union of countably infinite sets is countable
negative_passages.docid: 12436
negative_passages.text: The cardinality of the set of all finite subsets of an infinite set
negative_passages.docid: 40937
negative_passages.text: Is the set of partial order relations over $ \mathbb{N}$ countable?
negative_passages.docid: 82947
negative_passages.text: Undecidable cardinality
negative_passages.docid: 79974
negative_passages.text: The cardinality of Lebesgue sets
negative_passages.docid: 72750
negative_passages.text: Uncountable number of mutually disjoint countable sets in $\mathbb R$
negative_passages.docid: 94825
negative_passages.text: Open set as a finite union of closed sets
negative_passages.docid: 157513
negative_passages.text: How can I prove that these sets are countable infinite?