query: Sets containing itself and axiom of regularity
positive_passages.docid: 62208
positive_passages.text: If $A$ is a non-empty set, then $A \notin A$
negative_passages.docid: 272
negative_passages.text: Cantor Sets/nonempty/cardinality
negative_passages.docid: 65308
negative_passages.text: Axiom of Choice: Family of non-empty sets mutually disjoint or not?
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 67066
negative_passages.text: Proof there is a 1-1 correspondence between an uncountable set and itself minus a countable part of it
negative_passages.docid: 14512
negative_passages.text: Why cannot a set be its own element?
negative_passages.docid: 84485
negative_passages.text: What is the purpose of the Axiom of regularity/foundation?
negative_passages.docid: 19289
negative_passages.text: complement of a set and its measure
negative_passages.docid: 48820
negative_passages.text: Where is axiom of regularity actually used?
negative_passages.docid: 4213
negative_passages.text: The set that only contains itself
negative_passages.docid: 158882
negative_passages.text: Prove the existence of some weird family of sets
negative_passages.docid: 151521
negative_passages.text: Set Theory: Tree Property
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 54497
negative_passages.text: Set Notation - Inclusion and Proper Inclusion
negative_passages.docid: 81509
negative_passages.text: The cardinality of a countable union of countable sets, without the axiom of choice
negative_passages.docid: 70143
negative_passages.text: Mutually exclusive countable subsets of a countable set
negative_passages.docid: 9330
negative_passages.text: Meaning behind Filter in Set Theory