 Okay, here's my first attempt with a new camera, trying to do classifying real numbers. Let's see, Justin trying out the same thing. Talking balls. Nice. Okay, today we're going to talk about classifying real numbers. As you can see up here I have one, two, three, four, five different classifications for real numbers. Again, in mathematics we need to define everything. So what we're doing here is we're defining different groups of numbers. Okay, so first off we have the natural numbers. Natural numbers, you can also call those the counting numbers. That's what they're commonly referred to as. The natural numbers are your simplest ones. Your one, two, three, so on and so forth. The three little dots mean so on and so forth in that fashion. So one, two, three, that's what we call the natural numbers. Back in the day these natural numbers were used to count your flock of sheep or your cattle or whatever it is that you had. Alright, next classification we have is the whole numbers. Whole numbers are very similar to the natural numbers. It actually just includes one other number. That number would be zero. Zero, one, two, three, so on and so forth. Okay, so the only difference between natural numbers and whole numbers is that whole numbers has one extra number. Simply just zero. Next we have the integers. One way you can think of the integers as is the whole numbers plus all the negative numbers. So now we're starting to introduce negative numbers into our classification. So for example, now I'm going to use the dots here again. Dot, dot, dot, negative three, negative two, negative one, zero, one, two, three, so on and so forth. Now notice that I have dots at both ends of these. That means so on and so forth to the left and so on and so forth to the right which means the integers include all these numbers plus all the way to negative infinity and all the way to positive infinity. So these are all the numbers that you guys are used to working with that a lot of kids like to do math problems and get whole numbers. They are positive or negative numbers. These are the integers that usually kids like to work with. Next, second to last year is the rational numbers. One way I like to think of rational numbers as is rational numbers are fractions. So far we've looked at everything. It just looks like a number. Now we're going to start defining our fractions. Rational numbers is any number that you can make into a fraction. So for example, three-fifths, negative twelve-sevenths. Just about anything is going to be a rational number. Even eight over four. Now when that pops into your head, when I say eight over four, you should think to yourself, well doesn't that reduce? Yes it does which means if you take eight divided by four, eight divided by four, you get two. So that means that two is also a rational number. You can take your whole numbers, either your integers, your whole numbers, your natural numbers, you can take any one of those and make them into a fraction. So that means our natural numbers, our whole numbers, our integers, they are all rational numbers because we can make them into fractions. Another classification, another different type of number that is also a rational number, and these are ones that are a little bit weird, these would be your non-terminating, use a little bit of vocabulary here, non-terminating repeating numbers. So for example, one-third is a rational number. Now that doesn't look like a repeating decimal, but if you take one-third, plug it into a calculator, whatever it is, you also know that one-third is equal to point three repeating. Point three, three, three, three, three, three, three, so on and so forth forever. So that repeating decimal, even though that number goes on forever and ever and ever, it's still a rational number because we can take that repeating decimal and turn it back into a fraction. So those are the first four classifications of numbers. Those are the ones you'll be hearing for most often. Now over to this other side, the irrational numbers. These ones are a little bit different. The most popular irrational number that you'll see is pi. Everybody knows what pi is, 3.1414159, so on and so forth. Now the difference between pi and something like point three repeating, we all know pi goes on forever, it just keeps going on forever and ever and ever. Just random numbers, they just keep going, they keep accumulating. There's no pattern to any of these numbers. So for pi, since there is no pattern, we call that an irrational number. No pattern, irrational number. Whereas point three repeating, yes, it does go on forever, but there's a pattern to it, so that makes a rational number. So pi is your irrational number. Anything, any number that you can think of that has no pattern to it is going to be an irrational number. Pi is just the more famous of the irrational numbers that we have. And so those are your five classifications of real numbers, natural numbers, whole numbers, integers, rational numbers, and then also irrational numbers.