Formulas & tables/Mathematics/Absolute value/Definition of absolute value
Definition of absolute value

Definition of absolute value

∣a∣={a,a≥0−a,a<0|a|=\begin{cases}a,&a\ge 0\\-a,&a<0\end{cases}

Result unit: — (liczba $\ge 0$)

What it describes

The absolute value is the distance of a number from zero on the number line — always non-negative.

Symbols

aa
real number

Where it comes from

The absolute value is the distance of a number from zero — always non-negative. For a positive number it is the number itself, for a negative number — its opposite.

When to use it

Distances on the number line, the modulus, defining functions piecewise.

Example

Compute ∣−5∣|-5| and ∣3∣|3|.
Substitution−5<0-5<0, 3≥03\ge0.
Result∣−5∣=5|-5|=5, ∣3∣=3|3|=3.

Related formulas

Properties of absolute value Inequalities with absolute value

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