# Order and Absolute Value

Order of Real Numbers

Let and be two real numbers. Then
is less than , written if is to the left of .
is less than , written if is to the right of .

Variations of and :
-- less than or equal to
-- greater than or equal to
-- not less than
-- not greater than

An inequality is a statement involving symbols , , , , , , , . Ex. , , .

The inequality says that is between and .

Absolute Values of Real Numbers

The absolute value of a real number is the distance from the number to 0 on the number line. The absolute value of is written as . For all real numbers

Ex. ,

Properties of absolute values For all real numbers and :

1.
2.
3.
4. ,
5. (triangle inequality)

Distance between two points on a number line Let P and Q be two points on the number line with coordinates and respectively. Then the distance between and is .

Subsections

Department of Mathematics