And the reason why this matters is if this wasn't the case, if f of 0 wasn't the same as the limit, then we might have a gap right over there. So you could have limits. So you could have a situation like this, where you have a gap right over there. And then it looks something like that. So the two limits from the left and the right both exist. And the limit at that point would exist. But if the function itself does not equal that value there, if it equals something else, then the function would not be continuous.