How do I show this inequality: $|x - y | \le |x| + |y| $?
Somehow use the triangle inequality?
How do I show this inequality: $|x - y | \le |x| + |y| $?
Somehow use the triangle inequality?
Apply triangle inequality for the vectors $\vec{x}$ and $-\vec{y}$ and recall that $\Vert -y \Vert = \Vert y \Vert$
\begin{eqnarray} |x-y| &\le & |x|+ |-y|&=& |x| + |y| \end{eqnarray}