query: Extract countable set from uncountable set
positive_passages.docid: 145471
positive_passages.text: $\Gamma \subset \mathbb{R}^{+}$ is uncountable. Can we choose a sequence from $\Gamma$ of which the sum is $\infty$
negative_passages.docid: 51674
negative_passages.text: use of $\sum $ for uncountable indexing set
negative_passages.docid: 97697
negative_passages.text: Countable union of sets of cardinality $c$ has cardinality $c$
negative_passages.docid: 48523
negative_passages.text: Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 44839
negative_passages.text: Better ways to get nth element from an unsubscriptable iterable
negative_passages.docid: 52682
negative_passages.text: Is the power set of the natural numbers countable?
negative_passages.docid: 127678
negative_passages.text: A partition of the unit interval into uncountably many dense uncountable subsets
negative_passages.docid: 119886
negative_passages.text: The cantor set is uncountable
negative_passages.docid: 51094
negative_passages.text: Prove that the set of integer coefficients polynomials is countable
negative_passages.docid: 139247
negative_passages.text: Real Analysis - Prove a set is countable
negative_passages.docid: 152523
negative_passages.text: NSCountedSet - get count of items in set
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: 36184
negative_passages.text: Countability of disjoint intervals
negative_passages.docid: 63276
negative_passages.text: Is an arbitrary union of a chain of countable sets countable?
negative_passages.docid: 67451
negative_passages.text: Building a bijection from a finite union of countable sets to $\mathbb{N}$
negative_passages.docid: 28539
negative_passages.text: Does any uncountable set contain two disjoint uncountable sets?