query: Proving intersection of empty set is the set of all sets
positive_passages.docid: 27107
positive_passages.text: intersection of the empty set and vacuous truth
negative_passages.docid: 109229
negative_passages.text: An Example of a Nested Decreasing Sequence of Bounded Closed Sets with Empty Intersection
negative_passages.docid: 157753
negative_passages.text: Show that any set in a metric space can be written as the intersection of open sets
negative_passages.docid: 158671
negative_passages.text: Cardinality of a set that consists of all existing cardinalities
negative_passages.docid: 74311
negative_passages.text: Proving that the Intersection of any Collection of Compact Sets is Compact
negative_passages.docid: 21820
negative_passages.text: How to prove that a set is invariant?
negative_passages.docid: 62709
negative_passages.text: Functions that are sets of all function - proofs
negative_passages.docid: 32441
negative_passages.text: How to prove or disprove statements about sets
negative_passages.docid: 113083
negative_passages.text: How to prove a set equality?
negative_passages.docid: 36881
negative_passages.text: Empty intersection and empty union
negative_passages.docid: 106756
negative_passages.text: Union and Intersection of Sets $A_{i}$ and $B_{j}$
negative_passages.docid: 118595
negative_passages.text: Proving that a set is countable by finding a bijection
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: 136108
negative_passages.text: Arbitrary intersection of closed, connected subsets of a compact space connected?
negative_passages.docid: 42145
negative_passages.text: Prove that the only sets in $R$ which are both open and closed are the empty set and $R$ itself.
negative_passages.docid: 152921
negative_passages.text: Proving that Unit Intersection is NP-complete
negative_passages.docid: 61930
negative_passages.text: Intersection of Closed and Compact Set is Closed