For every $a, b, x \in \mathbb{R}$ such that $a \le x \le b$, we have $|x| \le \max\{|a| , |b|\}$
105768
Proof involving absolute value and maximums
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
83124
Maximize :: $A = B \times C$
138283
$|(a,b)| = |\Bbb R|$ ? Cardinality of any open interval
93076
When $\min \max = \max \min$?
53378
$\max(\{n: n+5 | n^5 + 5\})$
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
29679
Prove: $|x-y|\leq |x|+|y|$
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
155884
What are the conditions on $\text{tr}(AB) \leq \text{tr(A)} \text{tr(B)}$ to be true?
3820
Prove that $||x|-|y||\le |x-y|$
96127
Maximum of $|\sin(z)|$ as $\{z: |z| \leq 1 \} $
108084
Is it always true? $\left|A-B\right| \le \left|A\right| + \left|B\right|$
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
145397
How to prove that for every $i$, $a_i = i$
52711
Prove that the sequence $\{v_n\}$ converges to the maximum value of $f$ on $[a,b]$
127242
$|A\times B|= \text{max}(|A|,|B|)$ for infinite sets