I am reading this lecture. Therefore, I am asking the following question in terms of what the lecture states, and not in terms of what any other individual or group advocates, because I need to answer the assessment questions related to the lecture, and not personal opinions. (The reason I clarify this is that I am aware that a lot of things regarding definitions in math are debated, and this is a definition question.)
According to the lecture whose link is provided above, "a function is increasing on an interval $I$ if, for any pair of points, $x_1<x_2$ in $I$, $f(x_1)<f(x_2)$." Now, if I test every single pair of points on the graph $f(x)=x^3$, $x_1$ is always smaller than $x_2$, so the function is increasing on its entire domain, as far as I understand. Am I correct? If so, it is correct to say that $f(x)$ is increasing on $I(-1,1)$.
However, if you look at the Answer section for Question 1.b in the Exercises section (you can navigate to those sections using the sidebar), it is clear that $x=1$ is excluded from the list of points which can be used in pairs to test the statement above (that regarding the definition of increasing intervals). I feel like there is some sort of contradiction here, unless I am misinterpreting something in the lecture.
Any clarification would be greatly appreciated.