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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 2 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 the 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 want to compare them so clearly 3 & 1 are not equal in fact I can make that statement with a not equal sign so I could say 3 does not equal 1 but let's say I want to figure out which one is larger and which one is smaller so if I want to 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 this means greater than the larger quantity the larger quantities on the opening the larger on the the larger I guess if you could view this as some type of an arrow or a [ __ ] well some type of symbol that this is the bigger side here you have this little teeny tiny point and here you have the big side so the larger quantities on the big side this would literally be read as 3 is greater than so let me write that down greater then 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 1 1 right over there this is making a comparison but if 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 want to say 5 is less than 19 so I would want to say let me write that down I want to write 5 is less than 5 is is less than is less than 19 that's what I want to 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 then it makes complete sense that 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 five 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 five is less than 19 five is a smaller quantity than nineteen I could also write this as I could write 1 plus 1 is less than 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