query: Why can a set not contain itself?
positive_passages.docid: 50258
positive_passages.text: How can a set contain itself?
negative_passages.docid: 125077
negative_passages.text: what is the absolute value of a set?
negative_passages.docid: 54497
negative_passages.text: Set Notation - Inclusion and Proper Inclusion
negative_passages.docid: 36721
negative_passages.text: Is "The empty set is a subset of any set" a convention?
negative_passages.docid: 152382
negative_passages.text: Can an infinite set A be larger than an infinite set B but still have the same cardinality?
negative_passages.docid: 125317
negative_passages.text: Is this statement "Every element in the empty set is greater than itself." true or its negation is true?
negative_passages.docid: 30660
negative_passages.text: Empty set does not belong to empty set
negative_passages.docid: 36281
negative_passages.text: A set is infinite iff it is equivalent to a proper subset of itself
negative_passages.docid: 121847
negative_passages.text: Don't we need the axiom of choice to choose from a non-empty set?
negative_passages.docid: 71653
negative_passages.text: Why is the Cartesian product of a set $A$ and empty set an empty set?
negative_passages.docid: 135656
negative_passages.text: Why non-measurable sets exist?
negative_passages.docid: 89749
negative_passages.text: Example of a not recursively enumerable set $A \subseteq \mathbb{N}$
negative_passages.docid: 2935
negative_passages.text: Completness and Set of Result of One Set ?!?
negative_passages.docid: 62208
negative_passages.text: If $A$ is a non-empty set, then $A \notin A$
negative_passages.docid: 50846
negative_passages.text: Is a set without limit points necessarily closed?
negative_passages.docid: 33117
negative_passages.text: Cyclic containment of sets
negative_passages.docid: 99480
negative_passages.text: Why is predicate "all" as in all(SET) true if the SET is empty?