Arithmetic : Real Numbers

Absolute Value and Opposites

The absolute value of a number n is denoted by |n|.
It is defined as the distance between 0 (zero) and n (the number) on the number line.
Importantly, the absolute value of any nonzero number is always positive.
For example, |1.5| = 1.5 and |−1.5| = 1.5.
Both 1.5 and −1.5 have the same absolute value of 1.5, because 1.5 is 1.5 units from 0 (to the right) on the number line and −1.5 is 1.5 units from 0 (to the left).
Thus, |−n| = |n| for any nonzero number n, and |0| = 0.

Two unequal numbers with the same absolute value are called opposites.
For example, −1.5 is the opposite of 1.5, and 1.5 is the opposite of −1.5.
Note that the only number that is equal to its opposite is 0 (zero).