prove $|X-Y|\le|X|+|Y|$
7775
Show that $|x-y|\leq |x|+|y|$.
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
28822
$|x| - |y| \leq |x-y|?$
129584
How prove $E|X|^p<\infty$ and $E|Y|^p<\infty$, if $E|X+Y|^p<\infty$
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
12484
Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
122971
how to prove that $\ln(1+x)< x$
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
139711
prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
82961
Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$.
66707
How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $
126032
Proving a certain inequality
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
91877
Let $|x|\leq1, |y|\leq 1$. Show that$0 \leq x^{2}+y^{2} -2x^{2} y^{2}+2xy \sqrt{1-x^{2}} \sqrt{1-y^{2}} \leq 1$
77026
Proof with inequalities