ThmDex – An index of mathematical definitions, results, and conjectures.
Triangle inequality for absolute value function
Formulation 0
Let $t \mapsto |t|$ be the D412: Absolute value function.
Let $x, y \in \mathbb{R}$ each be a D993: Real number.
Then \begin{equation} \bigg| |x| - |x| \bigg| \leq |x - y| \leq |x| + |y| \end{equation}