prove by cases that $|r + s| \leq |r| + |s|$ for all real numbers.
104217
Alternative triangle inequality proof
1275
Prove that $a_1+\cdots+a_n \geq n$ if $a_1$, $a_2$, ... $a_n$ are positive real numbers and their product is $1$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
145397
How to prove that for every $i$, $a_i = i$
106011
Proving it has all real roots
7775
Show that $|x-y|\leq |x|+|y|$.
45090
Given any positive real numbers $a,b,c$, we have $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
108704
Help with proof of $|x+y| \geq |x|-|y|$
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
43478
Prove that: $ m_a + m_b + m_c \le 4R + r $
45619
Prove: $|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
51347
Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$