Absolute Value
The absolute value of a real number \(x\) is denoted by \(|x|\) and is defined as follows:
\[|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases} \]In other words, if the number is positive, the absolute value is the number itself, and if the number is negative, the absolute value is the number with the sign flipped i.e. the positive version of the number.
Example \[\begin{align*}
|3| &= 3 \\
|-3| &= 3 \\
|0| &= 0 \\
|-\frac{1}{2}| &= \frac{1}{2} \\
|5 - 7| &= 2 \\
|-3.14| &= 3.14
\end{align*}
\]
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