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The Integers. Definitions. 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? ).
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The Integers Definitions
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 signof the number.
The Basics • The game shows that -(-3) = 3, so 3 + (-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.
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.
