Use absolute value.


Use absolute value.

Geometrically, the absolute value of a number a, written 0 a 0, is the distance on the number line from 0 to a. For example, the absolute value of 5 is the same as the absolute value of

– 5 because each number lies five units from 0.  That is,

\left | 5 \right | = 5 and \left | -5 \right | = 5.

Absolute value



Because absolute value represents distance, and distance is always positive

(or 0), the absolute value of a number is always positive (or 0).


The formal definition of absolute value follows.

Absolute Value

\left | a \right | \left\{\begin{matrix}  a& if& a& is& positive& or& 0    & \\  -a& if& a& is& negative    &  \end{matrix}\right.


The second part of this definition, \left | a \right | = –a if  a is negative, requires careful

thought. If a is a negative number, then  – a, the additive inverse or opposite

of a, is a positive number, so \left | a \right |  is positive.

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