query: What is $\inf\emptyset$ and $\sup\emptyset$?
positive_passages.docid: 1307
positive_passages.text: Infimum and supremum of the empty set
negative_passages.docid: 858
negative_passages.text: Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?
negative_passages.docid: 9330
negative_passages.text: Meaning behind Filter in Set Theory
negative_passages.docid: 125502
negative_passages.text: Empty set literal?
negative_passages.docid: 130418
negative_passages.text: Is ${\{\emptyset,\{\emptyset\},\{\{\emptyset\}\},\{\{\{\emptyset\}\}\},...\}} $ a set?
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: 74440
negative_passages.text: How does the axiom of regularity forbid self containing sets?
negative_passages.docid: 152817
negative_passages.text: Proving $\sup B=\inf A$
negative_passages.docid: 124325
negative_passages.text: Element of, subset of and empty sets
negative_passages.docid: 79307
negative_passages.text: How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?
negative_passages.docid: 81203
negative_passages.text: Supremum and infimum of sets
negative_passages.docid: 68781
negative_passages.text: proving if $a \le b$ then $\sup(A) \le \inf(B)$
negative_passages.docid: 34099
negative_passages.text: Proving that the empty set is unique
negative_passages.docid: 34580
negative_passages.text: FIND_IN_SET() vs IN()
negative_passages.docid: 112523
negative_passages.text: Does $\sqsubset$ have any special meaning?
negative_passages.docid: 152354
negative_passages.text: Why is an empty set not a terminal object in categories $\mathsf{Top}$ and $\mathsf{Sets}$?
negative_passages.docid: 136755
negative_passages.text: Direct proof of empty set being subset of every set