Formulas & tables/Mathematics/Absolute value

Absolute value

3 formulas · Mathematics

Definition of absolute value
∣a∣={a,a≥0−a,a<0|a|=\begin{cases}a,&a\ge 0\\-a,&a<0\end{cases}
Properties of absolute value
∣a⋅b∣=∣a∣∣b∣,∣ab∣=∣a∣∣b∣|a\cdot b|=|a||b|,\quad \left|\tfrac{a}{b}\right|=\tfrac{|a|}{|b|}
Inequalities with absolute value
∣x−a∣≤r  ⟺  a−r≤x≤a+r|x-a|\le r \iff a-r\le x\le a+r