But if I had a function that looked somewhat different than that, if I had a function that looked like this, let's say that it is defined up until then, and then there's a bit of a jump, and then it goes like this, well, this would be very hard to draw, this function would be very hard to draw going through X equals C without picking up my pen. Let's see, my pen is touching the screen, touching the screen, touching the screen, how do I keep drawing this function without picking up my pen? I would have to pick it up, and then move back down here, and so that is an intuitive sense that we are not continuous in this case right over here. 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.