Well, in order for the function to be continuous, if I had to draw this function without picking up my pen, well, the value of the function at that point should be the same as the limit. This is really just a more rigorous way of describing this notion of not having to pick up your pencil, this notion of connectedness, that you don't have any jumps or any discontinuities of any kind. So with that out of the way, let's discuss continuity over intervals. Let me delete this really fast so I have space to work with. So we say, so I'm gonna first talk about an open interval, and then we're gonna talk about a closed interval, because a closed interval gets a little bit more involved. So we say f is continuous over an open interval from a to b. So the parentheses instead of brackets, this shows that we're not including the endpoints.