Prove that $||x|-|y|| \leq |x-y|$
50273
How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
96133
Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $.
108704
Help with proof of $|x+y| \geq |x|-|y|$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
7775
Show that $|x-y|\leq |x|+|y|$.
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
20863
how do I prove this inequallity?
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
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 $Y$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
4498
Proof that $\|fx\| \leq \|f\|\cdot\|x\|$
109778
Proving $(x-c)|(p(x)-p(c))$