What is the VC dimension of $k$ finite unions of one-sided intervals:
If we take 3 one-sided intervals like $(-\infty, a_1] $, $(-\infty, a_2] $ and $(-\infty, a_3] $, I think union of these intervals can shatter $4 $ points as below, assuming that $a_1>a_2>a_3>a_4$:
Point $p_1$ at interval $(-\infty, a_1]$
Point $p_2$ at interval $[a_1, a_2]$
Point $p_3$ at interval $[a_2,a_3]$
Point $p_4$ at interval $(-\infty, a_3]$
For $k$ finite unions I think answer is $k+1$, am I right?