the integers definitions. think about the game! when working with negative numbers, think about what...
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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