query: $\overline{A\cdot B}=\overline{A}\cdot\overline{B}$ for $A,B\subseteq\Bbb R$?
positive_passages.docid: 22854
positive_passages.text: Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?
negative_passages.docid: 62172
negative_passages.text: Why does $-b < a < b \iff |a| < b$?
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: 39708
negative_passages.text: Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
negative_passages.docid: 14491
negative_passages.text: Verify the following relationship: $\nabla \cdot (a \times b) = b \cdot \nabla \times a - a \cdot \nabla \times b $
negative_passages.docid: 111515
negative_passages.text: Proving that $-a=(-1)\cdot a$
negative_passages.docid: 134770
negative_passages.text: For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
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: 13415
negative_passages.text: How to show if $A \subseteq B$, then $A \cap B = A$?
negative_passages.docid: 140628
negative_passages.text: Are $(\Bbb R,+)$ and $(\Bbb Q, +)$ elementary equivalent?
negative_passages.docid: 45405
negative_passages.text: An elementary way to show any bounded subset of $\Bbb{R}^k$ is totally bounded
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: 104068
negative_passages.text: Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
negative_passages.docid: 62342
negative_passages.text: $x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
negative_passages.docid: 80009
negative_passages.text: Prove that $| |a|-|b| | \le |a-b|$
negative_passages.docid: 102042
negative_passages.text: If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$
negative_passages.docid: 96845
negative_passages.text: Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$