 Hello, this is Chi-Chou again. Now I wanted to do a little introduction video for the next batch of videos that are going to be coming up in the next few days. What I ended up doing when I decided to do, you know, a series on the equal signing units, I opened up a gigantic can of words because the section is huge, right? Because there's all types of equations you're going to get and the equations are just a small part of the puzzle. The equations, you can think of functions, but functions in a special case where the y value is equal to zero. So you're trying to find x-intercepts. Whenever they say solve an equation, what you're doing is you're trying to find the x-intercepts for a function. Now we'll get into that when we start talking about functions and I do talk about it a little bit in these videos that I've already shot that I'm working on. So what I ended up doing, because this is a lot of material that I needed to cover, what I ended up doing instead of going around town finding walls because I would be, you know, I just wanted to keep it consistent, I ended up going to UBC and commandeering a lecture hall and classroom and ended up doing all the videos and I still doing some work there, doing the videos in the classroom. I'm going to be using a real chalkboard in a lecture hall. It's still going to look small and a little screen, but that's where I'm going to be doing the videos, that's where the videos are coming from. So what I ended up doing was starting off with basic equations and taking it up to higher level equations. What's going to be coming up is the first batch of videos is going to be the first type of equations we're going to get, which are simple equations where you can isolate the x and you get a value for x, where it's just x on one side. The equation could be gigantic, but you can combine all the x's so that you only have one x on one side and that equals a number. So we're going to have some examples of those types of equations. And then we started doing, or the videos that are going to be coming up, they're going to talk about quadratic equations. These are quadratic equations. And the way these work is it's x to the power of two. So for quadratic equation you need x to the power of two. You could have the single x value to the power of one or not. It doesn't make a difference. With these types of equations, as we've talked about before in series two, you can't combine the x squared and the x term because they're not identical. They don't have the same power. So there's new techniques that we learn to be able to solve these equations. And these types of equations, if it's x to the power of two, the degree decides the maximum number of solutions, you end up possibly having two different types of solutions. You could have one, you could have two, or you could have none. So there's going to be a whole bunch of videos coming up talking about quadratic equations and how we solve quadratic equations. And what I decided to do is go one level higher and deal with equations with higher degrees than two. So we're going to have equations coming up of x to the power of five plus b to the power of zero. Anything, any type of equation where it's higher degree than x to the power of one, because x just means x to the power of one, x to the power of two. So I dealt with higher degree equations. And we're going to do some examples there and learn one technique which is called synthetic division and how to solve these types of equations. Now between all these, again I'm going through this stuff super fast in the videos because this is a huge subject. And in between these you should be doing a lot of examples if you're in a course dealing with these types of equations. You should be doing examples of these to get this down packed because it's, again, they're new techniques of how to work with the language of mathematics, how to move things around, how to get answers solutions to problems to equations. Equations you can think about as the precursor to functions because equations are really just functions where we're forcing the y value, which is this side of the equation, the y value to be equal to zero. So what we're really doing is finding x intercepts. And I go a little bit into this when I'm doing the videos and we will get into this stuff a lot more when we start getting into functions. Because this is just solving equations. It's just one small piece of the puzzle when it comes to the language of mathematics. But when it comes to us being able to model something in the real world or not the real world, the imaginary world or anything that we want to model. So this solving equation when this is equal to zero is just us forcing the function to be equal to something and finding the x values associated with the function. It's really related to the Cartesian coordinate system that we talked about x and y in series one. So what we're going to do is start putting functions in here and finding out where the solutions are. And the solutions are really where the function crosses the x axis or any other axis that we set up. We can force an axis to be so. As I stated before, zero and infinity are a huge concept. They basically define our limitations in mathematics or restrictions. What we can do in mathematics and what we can't do in mathematics. Where mathematics can take us and the information it can give us. And it's limitations of how much we can get, what type of information we can get from it. Now, as we talked about before, one of the restrictions we have in mathematics is that we can't divide by zero. Because what happens is our equations, our functions explode. So if you have one over zero, I've stated that this is approximately equal to infinity. And infinity isn't a number. It's a symbol telling us that this thing is exploding. Something goes haywire here and we don't know what the final answer for this is if we divide one over zero. We can do approximations and that's where we're going to get into. But exact values are not there. We don't know what happens when you divide by zero. Things explode, things go haywire, the language collapses. So we're going to use this property or this restriction when we're solving equations. And later on when we get into functions, what this does is creates asymptotes for us. So when we have a function and somewhere on the Cartesian coordinate system, you end up dividing by zero. What it does is creates an asymptote. So if we had a function, let's say you were coming off an asymptote here. Our function cannot touch or cross this line. It could appear on this side but you can't go over it. So this is sort of a boundary that you cannot go over or into. So a function may look like this. And it gets closer and closer to this line but it never touches this line. And solving equations, when we're solving equations, what we're going to do is use a property of zero to solve equations that have higher degrees than just one. And that property is, for example, if you have A times B times C times D is equal to zero. If you have four things or multiple things, multiplied together to give you zero, the only way this can occur is if at least one of these things is zero. And when we're solving equations, we don't know which one of these things is zero. So what we do is we solve for each one of them equaling zero. So what we do is set each one of these things equal to zero. Because we don't know which one is zero, right? D is equal to zero. And this is the property of zero that we're going to use to solve equations. So when we have x cubed times x minus 2, you know, x to zero, we've got three things here, three terms multiplied together to give you zero. So the way we solve for this is we set each one of these things equal to zero. So we go x cubed is equal to zero. x minus 2 is equal to zero. x plus 1 is equal to zero. And we solve for these things. So x is equal to zero. And this is a very powerful property of zero that comes up that we use in the language of mathematics to solve for equations, which is basically means to give us information about a function. If you get lost through any of the videos that we're doing, don't worry about it. I will go into detail in the stuff when I start doing functions. But one thing you can do, if you need me to cover anything more in the next batch of videos coming up, post comments preferably on YouTube because that's the most active. So post comments on YouTube and, you know, if anything needs further clarification, what I will end up doing is after zero and infinity section, if there's time left over, you know, in this shooting season, I'm breaking these down into shooting seasons based on the weather. So if there's still time left in this shooting season, I will go back and make additional videos to clear some stuff up.