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Sal introduces the greater than symbol ">" and the less than symbol "<". Created by Sal Khan.
Video transcript
Most of us are familiar with the equal sign from our earliest days of arithmetic. You might see something like 1 plus 1 is equal to 2. Now a lot of people might think when they see something like this that somehow equal means give me the answer. 1 plus 1 is a problem, equal means give me the answer, and 1 plus 1 is two. That's not what equal actually means. Equal is actually just trying to compare two quantities. When I write 1 plus 1 equals 2, that literally means, that what I have on the left hand side of the equal sign, is the exact same quantity as what I have on right hand side of the equal sign. I could have just as easily have written 2 is equal to 1 plus 1. These two things are equal. I could have written 2 is equal to 2. This is a completely true statement, these two things are equal. I could have written 1 plus 1 is equal to 1 plus 1. I could have written 1 plus 1 minus 1 is equal to, is equal to 3 Minus 2. These are both equal quantities. What I have here on the left hand side, this is, this is 1, 1 plus 1 minus 1 is 1, and this right over here is 1, these are both equal quantities. Now, I will introduce you to other ways of comparing numbers. These are, the equal sign is when I have the exact same quantity on both sides. Now we'll think about what we can do when we have different quantities on both sides. So let's say I have the number 3, and I have the number 1, and I wanna compare them. So clearly, 3 and 1 are not equal, in fact I can make that statement with a not equal sign, so I can say 3 does not equal 1, but let's say I wanna figure out which one is larger and which one is smaller. So, if I wanna have some symbol, where I can compare them, where I can tell, where I can, I can state which of these is larger. And the symbol for doing that is the greater than symbol, the greater than symbol. This literally would be read as 3 is greater than 1, 3 is a larger quantity. And if you need, if you have trouble remembering what this, that this means greater than, the larger quantity, the larger quantities on the opening, the larger on the, the, the larger, I guess if you could view this as some type of an arrow or, I guess a shet, well, some type of symbol. Then this is the bigger side. Here you have this little teeny tiny point, and here you have the big side so the larger quantity's on the big side. This would literally be read as 3 is greater than, so let me write that down. Greater than, 3 is greater than 1. And once again, it just doesn't have to be numbers like this, I could write an expression. I could write, I could write 1 plus 1 plus 1, is greater than, is greater than, let's say, well just one 1 right over there. This is making a comparison. But what if we had things the other way around? What if I wanted to make a comparison between 5, and let's say 19. So now the greater than symbol wouldn't apply, it's not true that 5 is greater than 19. I could say that 5 is not equal to 19, so I could still make, I could still make this statement, but what if I wanted to make a statement about which one is larger and which one is smaller? Well if in plain English, I would wanna say 5 is less than 19, so I would wanna say, let me write that down, I wanna write 5 is less than, 5 is, is less than is less than 19. That's what I wanna say, and so we just have to think of a mathematical notation for writing is, for writing is less than. Well if this is greater than it makes complete sense, and let's just swap it around, let's make, once again, the point point towards the smaller quantity and the big side of the symbol point to the larger quantity. So here 5 is a smaller quantity, so I'll make the point point there, and 19 is a larger quantity, so I'll make it open like this. And so this would be read as 5 is less than 19, 5 is a smaller quantity than 19. I could also write this as, I could write 1 plus 1 is less that 1 plus 1 plus 1. It's just saying that this statement, this quantity, 1 plus 1, is less than 1 plus 1 plus 1.