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Corollary: Properties of the Absolute Value

(related to Definition: Absolute Value of Real Numbers (Modulus))

The absolute value has the following properties¹:

1. \(|-x|=|x|\) for all \(x\in\mathbb R\).
2. \(|xy|=|x||y|\) for all \(x,y\in\mathbb R\).
3. \(|\frac xy|=\frac{|x|}{|y|}\) for all \(x,y\in\mathbb R\), \(y\neq 0\).

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4 5

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Footnotes