query: Is the empty set a superset of itself?
positive_passages.docid: 58594
positive_passages.text: Is the empty set a subset of itself?
negative_passages.docid: 20706
negative_passages.text: Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
negative_passages.docid: 47697
negative_passages.text: Russell's paradox: a set cannot contain its own powerset
negative_passages.docid: 123090
negative_passages.text: How to show that disjoint closed sets have disjoint open supersets?
negative_passages.docid: 143003
negative_passages.text: $\bigcup \emptyset$ is defined but $\bigcap \emptyset$ is not. Why?
negative_passages.docid: 97951
negative_passages.text: Is the void set (∅) a proper subset of every set?
negative_passages.docid: 89712
negative_passages.text: For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
negative_passages.docid: 43462
negative_passages.text: Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?
negative_passages.docid: 34099
negative_passages.text: Proving that the empty set is unique
negative_passages.docid: 65549
negative_passages.text: What is the cartesian product of an empty set of sets?
negative_passages.docid: 272
negative_passages.text: Cantor Sets/nonempty/cardinality
negative_passages.docid: 153551
negative_passages.text: Is the null set a subset of every set?
negative_passages.docid: 99480
negative_passages.text: Why is predicate "all" as in all(SET) true if the SET is empty?
negative_passages.docid: 39020
negative_passages.text: Why is empty set an open set?
negative_passages.docid: 125077
negative_passages.text: what is the absolute value of a set?
negative_passages.docid: 131983
negative_passages.text: Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
negative_passages.docid: 46317
negative_passages.text: What is an Empty set?