What Is a Symbol?

Video Transcript

"What is a symbol? Hi, my name is Jimmy Chang. I've been teaching college mathematics for nine years, and when it come to a symbol in math, well, it actually does have a definition, so let's get into that first and we'll get into some basic examples as to what some of those symbols would be like. So a symbol, by definition, is actually something representing something else by association. In other words, you take a letter or a symbol and it will take...it will represent something else. For example, if you have X or Y, those are...can be symbols for numbers. But if you want to use symbols to express operations, then here's a couple of examples for you. We've all seen this. This is clearly the addition symbol, and we all know, of course, the single slash horizontally to mean a subtraction symbol. But there's a couple of other things to express these other operations. For multiplication, this was used. Now, as you might imagine, that can also be construed as an X. One of the mathematicians back in the day, Leibniz, when he saw this symbol for multiplication, he argued with the person who came up with that because he said, "You might...people might get it confused with the variable -- the letter X." So it wasn't until a few years later that another mathematician came up with the dot to express multiplication. This way, if you use this notation -- the dot notation -- you'll never get it confused with the X ever again. Rounding out the four operations, we have division. Now, division is probably one of the more flexible uses of notation because you're never going to get it confused with any other letter, per se, but there's other ways to express that. For fraction bars, this can be expressed as a division because four over two is thought of as four divided by two, but you can also express division another way by writing division in a diagonal fashion, as in four diagonal slash two. But you can use symbolism to express just about anything you're looking for, as long as you're clear about what it is that the symbol is representing. So I'm Jimmy Chang, and that is some examples of a symbol."