Category:Examples of Absolute Values

This category contains examples of Absolute Value.

Definition 1

Let $x \in \R$ be a real number.

The absolute value of $x$ is denoted $\size x$, and is defined using the usual ordering on the real numbers as follows:

$\size x = \begin{cases} x & : x > 0 \\ 0 & : x = 0 \\ -x & : x < 0 \end{cases}$

Definition 2

Let $x \in \R$ be a real number.

The absolute value of $x$ is denoted $\size x$, and is defined as:

$\size x = +\sqrt {x^2}$

where $+\sqrt {x^2}$ is the positive square root of $x^2$.