query: Does 'All countable unions' include 'all finite unions'?
positive_passages.docid: 157046
positive_passages.text: Finite union sigma field
negative_passages.docid: 146212
negative_passages.text: Can a union be initialized in the declaration?
negative_passages.docid: 52429
negative_passages.text: Explicit countable elementary extension of $\mathbb{N}$
negative_passages.docid: 136006
negative_passages.text: Prove that any countable cartesian product of countable sets is countable
negative_passages.docid: 31509
negative_passages.text: Is axiom of choice necessary for proving that every infinite set has a countably infinite subset?
negative_passages.docid: 19297
negative_passages.text: Is the cofinite topology on an uncountable set first countable?
negative_passages.docid: 78290
negative_passages.text: Countable axiom of choice: why you can't prove it from just ZF
negative_passages.docid: 32774
negative_passages.text: Finite Cartesian Product of Countable sets is countable?
negative_passages.docid: 14972
negative_passages.text: Cardinality of Vitali sets: countably or uncountably infinite?
negative_passages.docid: 23442
negative_passages.text: Cardinality of the union of infinite and countable sets
negative_passages.docid: 38711
negative_passages.text: When can uncountable nouns be countable?
negative_passages.docid: 106881
negative_passages.text: Does "finite" include zero?
negative_passages.docid: 13620
negative_passages.text: $\omega_2$ is a not countable union of countable sets without AC
negative_passages.docid: 152547
negative_passages.text: Is the sum of all natural numbers countable?
negative_passages.docid: 127200
negative_passages.text: Are there fields and ordered fields of every infinite cardinality?
negative_passages.docid: 113175
negative_passages.text: Why is the algebraic closure of a finite field countable?
negative_passages.docid: 128118
negative_passages.text: Is the cofinite topology on a countable set first countable?