The notation here really bothered me. The author defines the [closed, open) interval [a, b) as the list of all numbers number x that fulfill a ≤ x < b. Good so far, but when they talk about the empty interval [a, a) we get into problem because a ≤ x < a is a nonsensical statement. a cannot be equal to and strictly less then it self.

I think this is a problem when borrowing math concepts to programming. What the author is really talking about here is slicing, not intervals, and the slicing behavior is hopefully well defined on the construct you are working with, most of the time in a manner that makes sense to each construct, or in a consistent manner to other related constructs in the language.

If the author would stick with programming concepts, I don’t think this is a rule we should abide to, rather, a guideline which can be employed. And I think most programmers value consistency, so this really isn’t that much of an issue.