query: Why does $\|x\|_2 \le \|x\|_1$?
positive_passages.docid: 22129
positive_passages.text: Why is $\sqrt{\sum_{i=1}^n |v_i|^2} \leq \sum_{i=1}^n |v_i|$ true?
negative_passages.docid: 79024
negative_passages.text: the derivation of E(X|X)
negative_passages.docid: 122115
negative_passages.text: Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
negative_passages.docid: 16779
negative_passages.text: Why does $\left\| {\left| A \right|} \right\| \le \left\| {\left| I \right|} \right\|$, for every doubly stochastic matrix $A \in M_n$?
negative_passages.docid: 27564
negative_passages.text: Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
negative_passages.docid: 100968
negative_passages.text: Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
negative_passages.docid: 39082
negative_passages.text: Proving $x^\alpha-\alpha x \le 1- \alpha $
negative_passages.docid: 124208
negative_passages.text: Proof $|\sin(x) - x| \le \frac{1}{3.2}|x|^3$
negative_passages.docid: 116056
negative_passages.text: Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
negative_passages.docid: 34913
negative_passages.text: Why does basic algebra provide one value for $x$ when there should be two?
negative_passages.docid: 90896
negative_passages.text: proof of inequality $e^x\le x+e^{x^2}$
negative_passages.docid: 27969
negative_passages.text: Why does $\frac{1}{x} < 4$ have two answers?
negative_passages.docid: 16550
negative_passages.text: Is $ d(X) \le s(X)? $
negative_passages.docid: 151805
negative_passages.text: Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$
negative_passages.docid: 101486
negative_passages.text: Understanding that $A = \{x\in \ell_2: |x_n| \leq \frac{1}{n}, n = 1,2,...\}$ is compact in $l_2$.
negative_passages.docid: 84597
negative_passages.text: Derivative of $(1-x)^{-2}$
negative_passages.docid: 98921
negative_passages.text: Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?