Proof of $||a|-|b||\leq |a-b|$
81618
Prove $||a|-|b| | \leq |a-b|$
37924
Equivalence of norms proof
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
106979
Prove the inequality and limitation
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
28822
$|x| - |y| \leq |x-y|?$
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
152817
Proving $\sup B=\inf A$
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
65297
Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2} \right |\leq \left |b-c \right |$.
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
83714
$A \in B$ vs. $A \subset B$ for proofs