Definition

An integer : A whole number that can be either greater than 0, called positive, or less than 0, called negative. Zero is called the origin, and it's neither negative nor positive.

Opposites : Two integer that lie the same distance from the origin in opposite direction.

Number line:

The arrows on each end of the number line show us that the line stretches to infinity in both the negative and positive direction. We don't have to include a positive sign (+) when we write positive numbers. However, we do have to include the negative sign (-) when we write negative numbers.

Every number on the number line also has an absolute value, which simply means how far that number is from zero. The symbol for absolute value is two vertical lines. Since opposites are the same distance from the origin, they have the same absolute value. The absolute value of a negative number is its opposite, but the absolute value of a positive number is itself. The absolute value of zero is zero.

Examples:

Integers

• 3  is less       than  7    because  3   lies to the left of 7    
• -3 is greater  than -7   because -3  lies to the right of -7   
• -5 is less       than  4    because -5  lies to the left of 4    
• 5 is greater   than -4   because  5   lies to the right of -4   

Absolute Value

•  |-6| = |6|
•   |7| = |7|
•  |-5| is greater then |4| because the Absolute value of |-5| = 5 and the absolute value of |4| = 4