query: What is the cartesian product of a nonempty set and an empty set
positive_passages.docid: 125161
positive_passages.text: Why is the Cartesian product of $A$ and $\varnothing$ empty?
negative_passages.docid: 6161
negative_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 155777
negative_passages.text: Show that infinite Cartesian product is uncountable
negative_passages.docid: 123498
negative_passages.text: Is "empty set" an element 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: 19414
negative_passages.text: Uncountable subset with uncountable complement, without the Axiom of Choice
negative_passages.docid: 74860
negative_passages.text: Why is the empty set a subset of every set?
negative_passages.docid: 141806
negative_passages.text: Prove that a nest of sets has an empty intersection
negative_passages.docid: 62208
negative_passages.text: If $A$ is a non-empty set, then $A \notin A$
negative_passages.docid: 82315
negative_passages.text: is an empty set an element of {empty set}
negative_passages.docid: 154698
negative_passages.text: Union of Cartesian products: $X \times (Y \cup Z)= (X \times Y) \cup(X\times Z)$
negative_passages.docid: 51206
negative_passages.text: If $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set.
negative_passages.docid: 65768
negative_passages.text: What is the cardinality of the set of the empty set?
negative_passages.docid: 25553
negative_passages.text: elementary set theory (cartesian product and symmetric difference proof)
negative_passages.docid: 14711
negative_passages.text: set theoretic function, products of sets (product versus Cartesian product)
negative_passages.docid: 16056
negative_passages.text: Is empty set element of every set if it is subset of every set?
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?