query: Given an arbitrary set $X$, can one always find an element outside $X$?
positive_passages.docid: 144303
positive_passages.text: There is no set of all sets..
negative_passages.docid: 84609
negative_passages.text: Unary intersection of the empty set
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 86518
negative_passages.text: Does $X$ have a lower bound?
negative_passages.docid: 125077
negative_passages.text: what is the absolute value of a set?
negative_passages.docid: 69838
negative_passages.text: Does a countably infinite power set exist?
negative_passages.docid: 111723
negative_passages.text: Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
negative_passages.docid: 105852
negative_passages.text: How to verify whether or not there exists a vector $x$ such that $Ax > 0$?
negative_passages.docid: 126015
negative_passages.text: Elementary number theory in sets
negative_passages.docid: 132532
negative_passages.text: Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
negative_passages.docid: 158882
negative_passages.text: Prove the existence of some weird family of sets
negative_passages.docid: 146560
negative_passages.text: Is there any uncountably infinite set that does not generate the reals?
negative_passages.docid: 21229
negative_passages.text: If an element is not in the set difference $A\setminus B \: \:?$
negative_passages.docid: 145781
negative_passages.text: Is the collection of all functions between two sets a set?
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: 113582
negative_passages.text: How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$
negative_passages.docid: 84751
negative_passages.text: How can it be possible to localize a ring at a set with zero divisors?