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Fungrim entry: 48fe10

∣∣a∣−∣b∣∣≤∣a−b∣\left|\left|a\right| - \left|b\right|\right| \le \left|a - b\right|
This relation is known as the reverse triangle inequality.
Assumptions:a∈C and⁡ b∈Ca \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
TeX:
\left|\left|a\right| - \left|b\right|\right| \le \left|a - b\right|

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("48fe10"),
    Formula(LessEqual(Abs(Sub(Abs(a), Abs(b))), Abs(Sub(a, b)))),
    Description("This relation is known as the reverse triangle inequality."),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC