query: continuum, cofinality must be uncountable
positive_passages.docid: 26671
positive_passages.text: Does this seemingly elementary question require König's theorem?
negative_passages.docid: 65473
negative_passages.text: How can something finite become infinite?
negative_passages.docid: 12449
negative_passages.text: How to formulate continuum hypothesis without the axiom of choice?
negative_passages.docid: 54262
negative_passages.text: When are infinities okay?
negative_passages.docid: 125411
negative_passages.text: Infinite set always has a countably infinite subset
negative_passages.docid: 118390
negative_passages.text: Symbol for the cardinality of the continuum
negative_passages.docid: 22391
negative_passages.text: Is the set of all pairs of real numbers uncountable?
negative_passages.docid: 97064
negative_passages.text: Dense set in an infinite cofinite space
negative_passages.docid: 85398
negative_passages.text: $\mathsf{ZF}$ is not finitely axiomatizable
negative_passages.docid: 86685
negative_passages.text: Example of a set $S$ that is countable, but the set of limit points is uncountable
negative_passages.docid: 66398
negative_passages.text: Union of a finite set and a countably infinite set is countably infinite
negative_passages.docid: 72750
negative_passages.text: Uncountable number of mutually disjoint countable sets in $\mathbb R$
negative_passages.docid: 60678
negative_passages.text: Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
negative_passages.docid: 44974
negative_passages.text: Infinite set and countable subsets
negative_passages.docid: 13620
negative_passages.text: $\omega_2$ is a not countable union of countable sets without AC
negative_passages.docid: 99854
negative_passages.text: Must an uncountable subset of R have uncountably many accumulation points?
negative_passages.docid: 70940
negative_passages.text: Homework - set theory infinite union