Tag: absolute-value

real analysis – Reverse Triangle Inequality Proof

The Question : 106 people think this question is useful I’ve seen the full proof of the Triangle Inequality \begin{equation*} |x+y|\le|x|+|y|. \end{equation*} However, I haven’t seen the proof of the reverse triangle inequality: \begin{equation*} ||x|-|y||\le|x-y|. \end{equation*} Would you please prove this using only the Triangle Inequality above? Thank you very much. The Question Comments :