Prove inequality $|\sqrt{x}- \sqrt{y}| \le \sqrt{|x-y|}$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
2504
Inequality $\left|\,x_1\,\right|+\left|\,x_2\,\right|+\cdots+\left|\,x_p\,\right|\leq\sqrt{p}\sqrt{x^2_1+x^2_2+\cdots+x^2_p}$
104125
How prove this inequality??
129331
Prove that $|x^p - y^p| \le p|x-y|(x^{p-1} + y^{p-1})$ provided that $1 \le p \lt \infty$ and $x, y \ge 0$
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
143072
Proving $|\sin x - \sin y| < |x - y|$
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
29198
How to prove the following inequality $|\prod_{i=1}^{i=n}a_i-\prod_{i=1}^{i=n}b_i| < n\delta$?
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
91877
Let $|x|\leq1, |y|\leq 1$. Show that$0 \leq x^{2}+y^{2} -2x^{2} y^{2}+2xy \sqrt{1-x^{2}} \sqrt{1-y^{2}} \leq 1$
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
3820
Prove that $||x|-|y||\le |x-y|$
110368
Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$
83531
Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
8207
Can I prove this inequality algebraically?
108704
Help with proof of $|x+y| \geq |x|-|y|$