query: Is the following inequality True or False?
positive_passages.docid: 24575
positive_passages.text: How to prove that $ \sum_{n \in \mathbb{N} } | \frac{\sin( n)}{n} | $ diverges?
negative_passages.docid: 75387
negative_passages.text: A proof that $1=2$. May I know why it’s false?
negative_passages.docid: 132595
negative_passages.text: $\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
negative_passages.docid: 58969
negative_passages.text: A proof for the inequality $\sum_{i=0}^{t-2}{\frac{1}{t+3i}} \leq \frac{1}{2} $ for all $t \geq 2$
negative_passages.docid: 147785
negative_passages.text: Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
negative_passages.docid: 118212
negative_passages.text: Is it true that $A^A\simeq P(A)$?
negative_passages.docid: 20863
negative_passages.text: how do I prove this inequallity?
negative_passages.docid: 107601
negative_passages.text: Use of inequality $1 - \cos (x) \leq x^2 /2$
negative_passages.docid: 2504
negative_passages.text: Inequality $\left|\,x_1\,\right|+\left|\,x_2\,\right|+\cdots+\left|\,x_p\,\right|\leq\sqrt{p}\sqrt{x^2_1+x^2_2+\cdots+x^2_p}$
negative_passages.docid: 48092
negative_passages.text: Inequality involving a finite sum
negative_passages.docid: 77493
negative_passages.text: Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
negative_passages.docid: 134535
negative_passages.text: Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
negative_passages.docid: 30386
negative_passages.text: Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
negative_passages.docid: 131543
negative_passages.text: inequality with three variables and condition
negative_passages.docid: 67851
negative_passages.text: Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?
negative_passages.docid: 147145
negative_passages.text: Interesting short Inequality
negative_passages.docid: 28822
negative_passages.text: $|x| - |y| \leq |x-y|?$