So we'll now think about the extreme value theorem, which we'll see is a bit of common sense. But in all of these theorems, it's always fun to think about the edge cases. Why is it laid out the way it is? And that might give us a little bit of more intuition about it. So the extreme value theorem says if we have some function that is continuous over a closed interval, let's say the closed interval's from a to b. And when we say a closed interval, that means we include the endpoints a and b. That's why we have these brackets here instead of parentheses.