The IntegersThe IntegersThe IntegersThe IntegersDefinitionsDefinitions

Think about the game!

• When working with negative numbers, think about what it means in the MathGym-1D game.

• Which direction does the answer move something? (Is answer is positive or negative?)

• How far does it move it? (What is the size of the answer? )

What is an Integer?

• The integers are made up of the counting numbers, now called the positive integers: 1, 2, 3, 4, …

• The negative numbers-1, -2, -3, -4, …

• And zero 0

More Words to Learn

• We will use the capital letter Z (from the German word “zahlen”) to denote the set of integers.

• The positive numbers should be written as +1, +2, +3, +4, …, but we usually drop the + as unnecessary.

• The symbols + and – are called the sign of the number.

The Basics

• The game shows that -(-3) = 3, so3 + (-3) = 0 and (-3) + (-(-3)) = 0

• You can see that n + (-n) = 0

for every integer n.• Also

n + 0 = 0 + n = n for every n.

Absolute value• The absolute value or magnitude or

size of a number is how far it moves something, regardless of direction.

• Compute it by dropping the sign.• It is always greater than or equal to 0.

2 2

2 2

0.0001 0.0001

56.132 56.132

The Number Line• Lay out equally spaced points on a line and

label them with the integers:

• The numbers act just like street addresses, they tell you where to go.

• The arrow points in the positive direction.

• Later we will make up new numbers to give addresses to the other points.

-2-3 0-1 1 2 3

Work it out!

22

Work it out!

2 2

Work it out!

0 0

Work it out!

0 0

Work it out!

2 2

Work it out!

2 2

Work it out!

227 7

Work it out!

27 27

Work it out!

3 3.4567.4567

Work it out!

3.4567 3.4567

Work it out!

0.0003 0.0003

Work it out!

0.0003 0.0003

Work it out!

1,200,325 1,200,325

Work it out!

1,200,325 1,200,325

Work it out!

9 910 1,000,0( 10) 00,000

Work it out!

9 9 1,000( 10) ,000,00010

Work it out!

9 9( 10) 10 1,000,000,000