query: how do i prove that the the set of irrationals cannot be a countable union of closed subsets?
positive_passages.docid: 3296
positive_passages.text: Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
negative_passages.docid: 147534
negative_passages.text: The set of irrational numbers is not a $F_{\sigma}$ set.
negative_passages.docid: 88904
negative_passages.text: Help with a proof. Countable sets.
negative_passages.docid: 43894
negative_passages.text: If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable
negative_passages.docid: 23752
negative_passages.text: Proving Irrationality
negative_passages.docid: 23442
negative_passages.text: Cardinality of the union of infinite and countable sets
negative_passages.docid: 34998
negative_passages.text: How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 99478
negative_passages.text: countably infinite union of countably infinite sets is countable
negative_passages.docid: 132778
negative_passages.text: All distances are rational prove the set is countable
negative_passages.docid: 66398
negative_passages.text: Union of a finite set and a countably infinite set is countably infinite
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
negative_passages.docid: 132868
negative_passages.text: Bijection between an infinite set and its union of a countably infinite set
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 44974
negative_passages.text: Infinite set and countable subsets
negative_passages.docid: 120135
negative_passages.text: Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets
negative_passages.docid: 35837
negative_passages.text: How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?