**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

__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
.

Department of Mathematics