Proof $|x+y|+|x-y| \geq |x| + |y|$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
3820
Prove that $||x|-|y||\le |x-y|$
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
5222
$\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$
139711
prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
88328
Proof of $1+x\leq e^x$ for all x?
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
106979
Prove the inequality and limitation
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$
42516
If every $x\in X$ is uniquely $x=y+z$ then $\|z\|+\|y\|\leq C\|x\|$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
7775
Show that $|x-y|\leq |x|+|y|$.
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$