This is an open interval. So you can keep getting closer and closer and closer to b, and keep getting higher and higher and higher values without ever quite getting to b. Because once again, we're not including the point b. Similarly, you could get closer and closer and closer to a and get smaller and smaller values, but a is not included in your set, in your consideration. So f of a cannot be your minimum value. So that's, on one level, it's kind of a very intuitive, almost obvious theorem. But on the other hand, it is nice to know why they had to say continuous and why they had to say a closed interval like this.