1
$\begingroup$

How do I show this inequality: $|x - y | \le |x| + |y| $?

Somehow use the triangle inequality?

  • 0
    Oh wow..but thanks2012-07-01

2 Answers 2

3

Apply triangle inequality for the vectors $\vec{x}$ and $-\vec{y}$ and recall that $\Vert -y \Vert = \Vert y \Vert$

3

\begin{eqnarray} |x-y| &\le & |x|+ |-y|&=& |x| + |y| \end{eqnarray}