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The Integers Definitions

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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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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

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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.

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**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.

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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.

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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.

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Work it out!

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