To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
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 $Y$
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
126032
Proving a certain inequality
7775
Show that $|x-y|\leq |x|+|y|$.
108704
Help with proof of $|x+y| \geq |x|-|y|$
122944
Prove $|y''(x)| \leq 40$ for all $x \in [1,3]$.
67851
Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
77026
Proof with inequalities
42193
Show that $E(Y^p)=\int_{0}^{\infty}px^{p-1}P(Y\geq x)dx$
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
109778
Proving $(x-c)|(p(x)-p(c))$
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
106979
Prove the inequality and limitation
60761
Proof: $\cos^p (\theta) \le \cos(p\theta)$
14448
Elementary proof that $|x|^p$ is convex.
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?