But let's actually come up with a formal definition for continuity, and then see if it feels intuitive for us. So the formal definition of continuity, let's start here, we'll start with continuity at a point. So we could say the function F is continuous, continuous at X equals C, continuous at X equals C, if and only if, I'll draw this two-way arrow to show if and only if, the two-sided limit of F of X as X approaches C is equal to F of C. So this seems very technical, but let's just think about what it's saying. It's saying, look, if the limit as we approach C from the left and the right of F of X, if that's actually the value of our function there, then we are continuous at that point. So let's look at three examples. Let's look at one example where, by our picking up the pencil idea, it feels like we are continuous at a point, and then let's think about a couple of examples where it doesn't seem like we're continuous at a point, and see how this more rigorous definition applies. So let's say that my function, so let's say this right over here is, Y is equal to F of X, and we care about the behavior right over here when X is equal to C. This is my X axis, that's my Y axis.