How do you derive that | |x|-|y| |<= |x-y|
2026-03-30 08:15:16.1774858516
Algebra, analysis and inequality signs involving modulus signs
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If you already have the triangle inequality -
$$ |x| = |x-y+y| \leq |x-y| + |y|. $$
Subtract from both sides to conclude that
$$ |x| - |y| \leq |x-y|. $$