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Definitions
The document defines integers and their properties. Integers include positive numbers like 1, 2, 3, and their opposites -1, -2, -3, called negative numbers, as well as zero. The integers follow rules like -(-3) = 3, and for any integer n, n + -n = 0. Integers can be visualized on a number line with equally spaced points labeled with numbers, showing their relative positions and how they increase or decrease in the positive direction.
Definitions
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- 2. Think about thegame! 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? )
- 3. What is anInteger? 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
- 4. More Words toLearn 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.
- 5. The Basics Thegame 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.
- 6. 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.
- 7. The Number LineLay 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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