Video1: Real Number System

Hi, class. This is miss champagne, and today I'm going to teach you the real number system. These are just fancy words for numbers that you've been working with ever since you were two years old. So first I want you to think about how a two year old child would start counting. If you asked that child count, the child would say one, two, three, four, five. Those are called natural numbers. Those are numbers that just come out naturally. They are positive numbers only, that child may be able to count up to ten, 11, 12, 20, up to a thousand, 2000, a million. But all of those positive numbers are called natural numbers. When you're about from two years old to about four years old, you count using natural numbers. Now, when you get about 5 years old in kindergarten, that's when you're introduced to zero. So I'd say about 5 years old. So this is a natural progression. At 5 years old, now the child can say zero, one, two, three, four, 5, 6. That child now knows what zero means. So the only difference between natural numbers and whole numbers is that zero is considered a whole number is not considered something that a child naturally would say. So one is a natural number and one is also a whole number. So it's both. An integer, any positive whole number, zero, or negative number that you will find on the number line of coordinate plane. We have a number line that looks like this. It has a zero in the middle. You have your positive numbers on this side. You have your negative numbers on this side. All of these numbers that we see on the number line, the positive numbers to the right, the zero in the middle, the negative numbers to the left, all of these are called integers. And integers, people have told me different things. Mostly in middle school, you're introduced to integers, maybe like 6th grade, some people are introduced, a little bit earlier, but definitely by 6th grade you know what negative numbers are. With the natural numbers, a whole number of the integers, no fractions, no decimals. Okay? So let's ask ourselves if negative 8 is each one of these three numbers in addition to a real number. For now, all of the numbers that we learned about are called real numbers. Now this is going to change what you get to algebra two, but for right now, all the numbers that we learned about are real numbers. Until you get to algebra two and learn about imaginary numbers. But we'll discuss that later. All right, so let's look at negative 8. So as negative 8, a natural number that a child would normally say and counting. The answer is no. So negative 8 is not natural. Is negative 8 a whole number? Whole numbers are only positive numbers, so no. Negative 8 is not a whole number. Is negative 8 and integer? Yes. Negative 8 is a negative number. So we're going to put yes. It is an integer. Is negative 8 a real number. All the numbers that we learned about until algebra two, I'll call real numbers. So we're going to put yes. Negative 8 is a real number. Let's look at one over 8. Is one over 8, a natural number that a child would normally say. The answer is no. So one over 8 is not natural. What about a whole number? Is one over 8 a whole number? No, because it's a fraction. And we said no fractions. So it's not a whole number. Is one over 8 an integer? Is it one of these numbers that you would find in graphing on a number line? No. It is not an integer. And is one over 8, a real number? Yes. It is a real number. Let's look at 8 over one. First, let's go back to one over 8. One over 8 is a fraction. And you'll see a written like this as well. This is just a division line. All they did was take away the two dots. So we have one divided by 8. If you take out your calculators and you do one divided by 8, what number do you see?