I am really stuck in the following:
I want to show that for all $\alpha,\beta,\gamma\in\mathbb{R}$ the following is true:
$|\alpha+\beta-\gamma|+|\alpha+\gamma-\beta|+|\beta+\gamma-\alpha|\ge|\alpha|+|\beta|+|\gamma|$ I know that I have to proof by cases.
So if I consider $\alpha,\beta,\gamma>0$ don't I have to consider in this case $\alpha+\beta\ge\gamma$ and $\alpha+\beta\le\gamma$, too?
Anybody could help with this inequality? Thanks a lot!