For any real numbers \(x,y\in\mathbb R\), the following **reverse triangle inequalities** hold:

$(1)$ $|x+y|\ge |x|-|y|,$

$(2)$ $|x-y|\ge \left||x|-|y|\right|,$

| | | | | created: 2017-03-19 12:25:53 | modified: 2017-03-19 12:32:20 | by: *bookofproofs* | references: [581]

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[581] **Forster Otto**: “Analysis 1, Differential- und Integralrechnung einer VerĂ¤nderlichen”, Vieweg Studium, 1983