absolute value
The magnitude of a number regardless of its sign. Hence, the absolute value of a number "n" is always positive or zero, written as |n|. When the number "n" is represented on a number line, its absolute value is the distance from the origin to that number.

symbol space|n| = n if n > 0
symbol space|n| = -n if n < 0

symbol space|4.3| = 4.3
symbol space|-4.3| = 4.3

The following properties hold:

symbol space1) |ab| = |a||b|;
symbol space2) |a+b| < |a| + |b|;
symbol space3) |a-b| > ||a| - |b||;
symbol space4) for a > 0, |x| < a if and only if -a < x < a.

Related Terms: distance (between two points), number line, origin, positive, sign, zero

English | Espaņol