query: $\mathcal A$ is empty, what is $\bigcap_{S\in\mathcal A}S$?
positive_passages.docid: 27107
positive_passages.text: intersection of the empty set and vacuous truth
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: 73221
negative_passages.text: How can I form a bijection between $\mathcal P(A)$ and $2^A$.
negative_passages.docid: 3072
negative_passages.text: If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
negative_passages.docid: 55488
negative_passages.text: Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
negative_passages.docid: 15312
negative_passages.text: Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
negative_passages.docid: 65549
negative_passages.text: What is the cartesian product of an empty set of sets?
negative_passages.docid: 146891
negative_passages.text: Why is $\{\emptyset\} \not = \emptyset$?
negative_passages.docid: 136321
negative_passages.text: Show that if $\sup\big\{\sum\lvert\, f(a)\rvert\big\}  0\}$ is countable.
negative_passages.docid: 125957
negative_passages.text: What is the product of the empty set?
negative_passages.docid: 46056
negative_passages.text: If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
negative_passages.docid: 1162
negative_passages.text: Why $\{\mathbf{0}\}$ has dimension zero?
negative_passages.docid: 38860
negative_passages.text: $P(\limsup A_n)=1 $ if $\forall A \in \mathfrak{F}$ s.t. $\sum_{n=1}^{\infty} P(A \cap A_n) = \infty$
negative_passages.docid: 88823
negative_passages.text: How can the empty set be open in the definition of the cofinite topology?
negative_passages.docid: 110669
negative_passages.text: Linear span of the empty set
negative_passages.docid: 55995
negative_passages.text: Why is the supremum of the empty set $-\infty$ and the infimum $\infty$?
negative_passages.docid: 24107
negative_passages.text: Bijection $f:\mathcal{P}(A)\to(A\to \{0,1\})$