query: Infinite sequence of derived sets $A', A'', A''',...$
positive_passages.docid: 18527
positive_passages.text: Confusion on Derived Sets and the $n$-the Derived Set
negative_passages.docid: 128517
negative_passages.text: A recursive sequence is defined by...
negative_passages.docid: 89749
negative_passages.text: Example of a not recursively enumerable set $A \subseteq \mathbb{N}$
negative_passages.docid: 138768
negative_passages.text: Showing that the family of Borel sets is countably generated
negative_passages.docid: 125962
negative_passages.text: The set $A'$ is closed in a $T_1$ space
negative_passages.docid: 158882
negative_passages.text: Prove the existence of some weird family of sets
negative_passages.docid: 12436
negative_passages.text: The cardinality of the set of all finite subsets of an infinite set
negative_passages.docid: 55614
negative_passages.text: Prove that a set consisting of a sequence and its limit point is closed
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: 62687
negative_passages.text: Proving Cardinality of Cosets in Abstract Algebra
negative_passages.docid: 4912
negative_passages.text: Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
negative_passages.docid: 154796
negative_passages.text: Completeness of sequence of reals with finitely many nonzero terms
negative_passages.docid: 117561
negative_passages.text: A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
negative_passages.docid: 127242
negative_passages.text: $|A\times B|= \text{max}(|A|,|B|)$ for infinite sets
negative_passages.docid: 97064
negative_passages.text: Dense set in an infinite cofinite space
negative_passages.docid: 149673
negative_passages.text: Cardinality of an infinite union of finite sets
negative_passages.docid: 63276
negative_passages.text: Is an arbitrary union of a chain of countable sets countable?