query: Is the product of two sets well-defined if one is empty
positive_passages.docid: 109219
positive_passages.text: How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
negative_passages.docid: 148213
negative_passages.text: Given a topological space $X$, why are both $X$ and $\emptyset$ open and closed?
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: 39293
negative_passages.text: Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
negative_passages.docid: 44673
negative_passages.text: $M$ connected $\iff$ $M$ and $\emptyset$ are the only subsets of $M$ open and closed at the same time
negative_passages.docid: 27937
negative_passages.text: Cartesian Product of Two Countable Sets is Countable
negative_passages.docid: 88982
negative_passages.text: Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
negative_passages.docid: 132692
negative_passages.text: Nonempty set mapped to $\emptyset$ and vice-versa
negative_passages.docid: 103314
negative_passages.text: Let $\{K_n \}_{n \in \mathbb{N}}$ be a collection of sets, where $K_n = [n, \infty)$. Why is $\bigcap_{n \in \mathbb{N}} K_{n}$ empty?
negative_passages.docid: 123613
negative_passages.text: Double Complement of a set proof
negative_passages.docid: 41783
negative_passages.text: Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
negative_passages.docid: 51687
negative_passages.text: Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
negative_passages.docid: 65308
negative_passages.text: Axiom of Choice: Family of non-empty sets mutually disjoint or not?
negative_passages.docid: 97373
negative_passages.text: Is whether a set is closed or not a local property?
negative_passages.docid: 125957
negative_passages.text: What is the product of the empty set?
negative_passages.docid: 110677
negative_passages.text: How is an empty set truly "empty"?
negative_passages.docid: 31212
negative_passages.text: The existence of the empty set is an axiom of ZFC or not?