 As far as your concern, in high school, you cannot divide by zero. Because if you divide by zero, you get infinity and we cannot grasp what infinity means, okay? So zero is one on the end, one end of the spectrum. Actually, it's the pivot. You got infinity on one side and you got negative infinity on the other side. If you divide by zero, you get both. I'll talk about these later, okay? Now, that was one of the most crucial boundaries, discoveries, breakthroughs in mathematics for us to comprehend what zero was. I believe it was someone in India or Iran that actually came up with, or defined the number zero. That's the best way of saying it. We're able to define what the boundary is between natural numbers, counting numbers, zero, one, two, three, all the way up to infinity, or the new set, which was zero, one, two, three, okay? Now, this continued on for a while and then some genius came along and found out there was negative numbers. What the hell are negative numbers? Well, just imagine the same bar. Now, these sheepherders down here in the natural number set, or the natural number group, after a few hundred years, they really understood that you don't really have to be a sheepherder to do something else in life. So they understood that if somebody has no sheep, then, well, that's okay. They can still join the group. They won't have to do anything about it. Now, after a few hundred years, some genius comes along and finds negative numbers. What are negative numbers? Well, negative numbers is another Joe blow walking through the door, sitting down at the table, and John Alfred, Alfredo, whoever's sitting around the table, they're all talking about their sheep and whatever this guy who's got zero sheep talks about, maybe he's a carpenter or something. Now, some Joe blow sits down at the table and they try to size this guy up and say, hey, what do you do? What do you have? Do you have any sheep? He's like, no, I got no sheep. Are you a carpenter? No, no, no, man, I'm not a carpenter. Well, what are you here for? What are you doing? Well, he goes, I'm here to buy sheep because I have negative sheep. I owe sheep to people. Now, just imagine these sheepherders. If you owe somebody some sheep, you know, these people, if they owed anything, if they owed any products, anything to anyone, then there's no way they could feed their family. And if they owed sheep, then what were they doing? How did they end up owing sheep to people? So all of a sudden, you got negative numbers. So initially, we knew about the natural number set, one, two, three, okay? We moved up to the whole number set with us being able to define what zero was, not fully understanding, and we still don't fully understand it, but being able to define what zero was. Then you got another boundary up here, going from the whole number set to the integers, which includes the negative whole numbers. So integers are really just the whole numbers with the negative side included. Now, when they ask you questions in math, in high school math, and they ask you what group a number belongs to, you have to take it to the lowest level, okay? So if they ask you which group set does a number one belong to, you would say it belongs to the natural numbers because the natural numbers, the whole numbers includes the natural numbers, and the integers includes the whole numbers, which includes the natural numbers. Now, if they ask you what zero is, you can only go down as far as whole numbers, okay? You don't say it's a natural number, you say it's a whole number, it's implied that it also includes the integers and the rational numbers. What's rational numbers? Well, rational numbers, what they tell you in high school, which is, it's true, but it really doesn't define it properly. Most teachers do this anyway. They tell you that rational numbers are numbers that repeat or terminate. Repeat means it continues on. Like 2.0 is a rational number because it ends. 2.2 repeating, if it's two all the way continuing, is a rational number because it repeats. But the true definition of rational numbers, the one you should really grasp is rational numbers are any numbers that can be expressed as a fraction of integers of these guys. So, this whole group set is connected together, okay? Rational numbers super important because they start introducing fractions to you. So just imagine these sheepherders sitting there. They're talking about sheep. After a few hundred years, they fully grasp or not fully grasp, they try to deal with what the hell the number zero means. And then some guy comes along and says he actually owes sheep, so they try to figure out what the hell owing sheep means. So after a few hundred years they deal with that and then some Joe Blue walks through the door and says, you know, sits down on the table and they, you know, they're trying to figure things out. They're still in the mindset. What does this guy do? What does that guy do? What's going on? They're asking questions, human nature, okay? So, they ask the guy what he does and he says, well, I'm here to buy half a sheep. Now, these guys would all of a sudden start thinking about what the hell is a half a sheep mean? Well, maybe he's having a party. But these guys are used to killing a sheep and killing and, you know, barbecuing it, eating the whole sheep. What the, why would, you know, how big must the family be? Where is he taking this half a sheep? So all of a sudden fractions get introduced, do you understand? It's, it's, it was a new concept and it really expanded the abilities or what we're doing in mathematics. Zero still remains the most crucial aspect of the real number set, okay? Because it still gives science, physics, mathematics problems. So right now we've got natural numbers, whole numbers, integers, and rational numbers belonging to this half of the real number set. Now, keep in mind that if they ask you what a whole number is or what zero is, you say it's a whole number, you take it down all the way to the lowest level that you can. If they ask you what negative two is, you take it down to the integers because you can't take it down to the whole numbers. Whole numbers do not include negative numbers, okay? If they ask you what one over two is, it's a rational number. It's no longer an integer, it's not a whole number, it's not a natural number, okay? So keep that in mind. What we have on the other side is, whoop, is the irrational numbers. Now this line here, the pipe, is the division between these two guys. Now irrational numbers really took mathematics to a new level because what it did was introduce something that we had no grasp of, which is numbers that do not end. Rational numbers were numbers, or the simple definition is, numbers that repeat or terminate, okay? Irrational numbers are numbers that do not repeat and do not terminate. The true definition of rational numbers is, any number that can be expressed as a fraction of integers. Irrational numbers, numbers that cannot be expressed as a fraction of integers. So for example, the number pi, there's no way you could put two numbers on top of each other, two integers on top of each other, one divided by the other, to come up with 3.14 dot, dot, dot, dot, dot. The most crucial aspect of this whole thing, the real number set, the real number set is the prime numbers, okay? Now, if you understand prime numbers, you'll understand this whole thing, mathematics becomes simple. So what you gotta consider is, you have for the real number set, you have two distinct boundaries, which is the pipe. You've got the rational numbers, which includes the integers, the whole numbers and the natural numbers, and you've got the irrational numbers, which is completely separate from the rational numbers, okay? Talked about this further, but I gotta look around and find another board where I can talk to you about prime numbers. I'll be back.