As I read this lecture for being familiar with VC dimension we find on p. 8:
VC(half intervals in $\mathbb{R}$ ) = 1 .... no subset of size 2 can be shattered
VC(intervals in $\mathbb{R}$ ) = 2 .... no subset of size 3
It's not clear to me. I read on Wikipedia about the difference of Half Interval and Interval and why VC dimension are different.
For example can this set be half intervals or intervals?
$$ \{ (-\infty \le x \le a) \, \left|\, a \in \mathbb{R} \right. \} $$
Any direction or hint on this problem?