query: The set of all finite subsets of $\mathbb{N}$ is countable
positive_passages.docid: 41661
positive_passages.text: Show that the set of all finite subsets of $\mathbb{N}$ is countable.
negative_passages.docid: 99478
negative_passages.text: countably infinite union of countably infinite sets is countable
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 101669
negative_passages.text: Cardinality of the Set of all finite subset of $\mathbb{R}$
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: 68994
negative_passages.text: Countable closed sets
negative_passages.docid: 52682
negative_passages.text: Is the power set of the natural numbers countable?
negative_passages.docid: 139247
negative_passages.text: Real Analysis - Prove a set is countable
negative_passages.docid: 60424
negative_passages.text: Uncountable family of uncountable compact subsets of $\mathbb{R}$
negative_passages.docid: 120273
negative_passages.text: Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
negative_passages.docid: 42794
negative_passages.text: Prove that functions map countable sets to countable sets
negative_passages.docid: 139078
negative_passages.text: Infinite partition of $\mathbb N$ by infinite subsets
negative_passages.docid: 12436
negative_passages.text: The cardinality of the set of all finite subsets of an infinite set
negative_passages.docid: 85099
negative_passages.text: How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
negative_passages.docid: 132868
negative_passages.text: Bijection between an infinite set and its union of a countably infinite set
negative_passages.docid: 103769
negative_passages.text: The Cartesian product of a finite number of countable sets is countable
negative_passages.docid: 136006
negative_passages.text: Prove that any countable cartesian product of countable sets is countable