How do I show that $ ||x| - |y||\leq|x - y| $
3820
Prove that $||x|-|y||\le |x-y|$
102478
$X_n\leq Y_n$ implies $\liminf X_n \leq \liminf Y_n$ and $\limsup X_n \leq \limsup Y_n$
29679
Prove: $|x-y|\leq |x|+|y|$
1932
How to show this equality of $\rho(X,Y)$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
27911
How can I prove that $xy\leq x^2+y^2$?
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
116382
Showing convexity of a function with the restriction over an arbitrary line
8207
Can I prove this inequality algebraically?
106979
Prove the inequality and limitation
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
116851
Show that f(x) is convex
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
126165
Prove $|\arctan x - \arctan y|\leq |x-y|$
64096
Prove that $||z_1|-|z_2|| \leq |z_1-z_2|$.
152311
Proving expression$\geq 2$, where variables are $x,y,z$