We essentially try to come up with a way that given any epsilon, we can always come up with a delta. Another way is we're going to try to describe our delta as a function of epsilon, not to confuse you too much. Maybe I shouldn't use f again. Delta equals function of epsilon that is defined for any positive epsilon. You give me an epsilon, I just put it into our little formula, our little function box, and I will always get you a delta. If I can do that for any epsilon, that will always give you a delta where this is true, that if x is within that range of delta of c, then the corresponding f of x is going to be within epsilon of l, then the limit definitely exists. Let's try to do that.