What's the better proof for $|a| - |b|$ $\leq$ $|a - b|$
81618
Prove $||a|-|b| | \leq |a-b|$
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
1478
An inequality for powers of reals: $a^{1/n}-b^{1/n}<(a-b)^{1/n}$
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
7775
Show that $|x-y|\leq |x|+|y|$.
76347
Shorter proof for some equvalences
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
116811
Proofs with limit superior and limit inferior: $\liminf a_n \leq \limsup a_n$
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
96133
Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $.
50266
In the following figure prove that: $AK||BC$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
3820
Prove that $||x|-|y||\le |x-y|$