Could you help me to show that $$ |a-b-c|\geq |b|-|a|-|c| $$ ?
2026-03-31 18:18:10.1774981090
Reverse triangle inequalities with three elements
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$|b| = |-b| \leq |a-b-c| + |c-a|$ by the triangle inequality, so $|a - b - c| \geq |b| - |c-a|$. Then you just need the triangle inequality again to get $|c-a| \leq |a| + |c|$, so $|b| - |c-a| \geq |b| - |a| - |c|$.