The Absolute Value Function
Some definitions worth keeping in mind while studying for the next of proofs.
The Absolute Value Function
Let \(x \in \mathbf{R}\), then the absolute value of \(x\) is denoted \(|x|\) and is given by
$$
\begin{equation*}
|x| = \begin{cases} x \quad \ \ \ \text{if } x \geq 0 \\ -x \quad \text{if } x \lt 0\end{cases}
\end{equation*}
$$
Properties
Let \(x \in \mathbf{R}\), \(|x| \geq 0\).
For the proof, see this.
Let \(x \in \mathbf{R}\), \(-|x| \leq x \leq |x|\).
For the proof, see this.
References: