query: Is it possible that $A \approx B$ but $A/B \not \approx (e)$?
positive_passages.docid: 151047
positive_passages.text: a non trivial example: $G/H$ is isomorphic to $G$
negative_passages.docid: 100387
negative_passages.text: Using $\epsilon-\delta$ to prove that a limit is not a specific number
negative_passages.docid: 39953
negative_passages.text: $a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
negative_passages.docid: 99165
negative_passages.text: How to prove that for Brownian motion in $(a, b)$ $\mathbb{E}^x[\min(H_a, H_b)] = (x-a)(b-x)$?
negative_passages.docid: 88982
negative_passages.text: Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
negative_passages.docid: 83714
negative_passages.text: $A \in B$ vs. $A \subset B$ for proofs
negative_passages.docid: 105233
negative_passages.text: Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?
negative_passages.docid: 115004
negative_passages.text: If $x\notin\mathbb Q$, then $\left|x-\frac{p}{q}\right|<\frac{1}{q^2}$ for infinitely many $\frac{p}{q}$?
negative_passages.docid: 103744
negative_passages.text: Minimal $ab$ for Rational Number $a/b$ in an Interval
negative_passages.docid: 113614
negative_passages.text: Approximating the density of $S\cap[a,b]$ using a Folner Sequence of $A$, where $S \subseteq A$?
negative_passages.docid: 87265
negative_passages.text: If $(A-\lambda{I})$ is $\lambda$-equivalent to $(B-\lambda{I})$ then $A$ is similar to $B$
negative_passages.docid: 76826
negative_passages.text: Are there sets $A$ and $B$ such that $A \in B$ and $B \in A$?
negative_passages.docid: 88971
negative_passages.text: An approximate eigenvalue for $ T \in B(X) $.
negative_passages.docid: 31846
negative_passages.text: Does $\neg(x > y)$ imply that $y \geq x$?
negative_passages.docid: 115338
negative_passages.text: Example: satisfying $E(X_{n+1}\mid X_n)=X_n$ but not a martingale
negative_passages.docid: 153355
negative_passages.text: Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?
negative_passages.docid: 53443
negative_passages.text: Does $a_n \sim b_n$ imply $\sum_n a_n \sim \sum_n b_n$ for $a_n, b_n>0$?