Absolute:

Definition:

An absolute value is a mathematical concept that gives the magnitude or distance of a quantity from zero, regardless of its direction or sign. It always returns a positive value, representing the principal value. Absolute values are denoted by vertical bars enclosing the number.

Properties:

• Always produces a non-negative value.
• The absolute value of a number is equal to the number itself if it is positive or zero.
• The absolute value of a negative number is equal to its positive counterpart.
• The absolute value of zero is zero.
• It obeys the triangle inequality property: |a + b| ≤ |a| + |b|.

Example:

For instance, the absolute value of -5 is 5, since it represents the distance of -5 from zero on the number line. Similarly, the absolute value of 7 is 7, as 7 is already a positive value.

Usage:

Absolute values are used in various mathematical applications, such as solving equations involving absolute value, determining the magnitude of vectors, handling complex numbers, and defining distance metrics.