query: Is there a null set that is not a Borel set?
positive_passages.docid: 22356
positive_passages.text: Lebesgue measurable but not Borel measurable
negative_passages.docid: 32458
negative_passages.text: Does the rank-nullity theorem hold for infinite dimensional $V$?
negative_passages.docid: 1307
negative_passages.text: Infimum and supremum of the empty set
negative_passages.docid: 130418
negative_passages.text: Is ${\{\emptyset,\{\emptyset\},\{\{\emptyset\}\},\{\{\{\emptyset\}\}\},...\}} $ a set?
negative_passages.docid: 5022
negative_passages.text: Can a set containing $0$ be purely imaginary?
negative_passages.docid: 72654
negative_passages.text: If $(a_n)$ is a null sequence and $(b_n)$ is bounded, then $(a_nb_n)$ is a null sequence
negative_passages.docid: 104744
negative_passages.text: Can sets of cardinality $\aleph_1$ have nonzero measure?
negative_passages.docid: 113863
negative_passages.text: The non-existence of non-principal ultrafilters in ZF
negative_passages.docid: 110957
negative_passages.text: No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
negative_passages.docid: 44927
negative_passages.text: Finding rank-nullity of a given matices
negative_passages.docid: 41937
negative_passages.text: Can one construct a non-measurable set without Axiom of choice?
negative_passages.docid: 4213
negative_passages.text: The set that only contains itself
negative_passages.docid: 65549
negative_passages.text: What is the cartesian product of an empty set of sets?
negative_passages.docid: 101028
negative_passages.text: Irrational numbers and Borel Sets
negative_passages.docid: 107215
negative_passages.text: Is $\emptyset \in \emptyset$ or $\emptyset \subseteq \emptyset$?
negative_passages.docid: 124732
negative_passages.text: Finding a nonempty subset that is not a subgroup
negative_passages.docid: 78300
negative_passages.text: Showing a set is closed other than giving a counterexample?