Positive real number that is equal to x if x is positive and that is equal to –x if x is strictly negative.
Symbol
The symbol is “| |” which is read as: “the absolute value of”.
The absolute value of a real number corresponds to the distance that separates this number from the origin on a number line. The distance between 0 and –10 is the same as between 0 and 10.
The absolute value of x and –x is x and we can write: | –x | = | x | = x.
Properties
There are four laws governing the concept of absolute value:
- | 0 | = 0
- If x ≠ 0, | x | > 0
- | x × y | = | x | × | y |
- | x + y | ≤ | x | + | y |
Examples
- | –12 | = 12
- | 12 | = 12
Historical Note
The first person to use the absolute value symbol (like |24|) was Karl Weierstrass (1815-1897) in 1841 to represent the absolute value of a complex number a + bi like: |a + bi|.