Proving that ${-1 \leq \operatorname{Corr}(X,Y) \leq 1}$
44193
How can I simply prove that the pearson correlation coefficient is between -1 and 1?
4498
Proof that $\|fx\| \leq \|f\|\cdot\|x\|$
7775
Show that $|x-y|\leq |x|+|y|$.
50273
How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
122944
Prove $|y''(x)| \leq 40$ for all $x \in [1,3]$.
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
14677
Proving the exponential inequality: $x^y+y^x\gt1$
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
8207
Can I prove this inequality algebraically?
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
36374
Exercise 1.6.3 from Alon & Spencer's *The Probabilistic Method*: prove that $Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1]$ for i.i.d. real RVs $X$ and $Y$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
3820
Prove that $||x|-|y||\le |x-y|$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
28125
Showing that $1 - \frac{x^2}2\leq\cos x$, $\forall x \in \mathbb{R}$