VC Dimension Calculation for Intervals
Yes, an open interval in $\mathbb{R}$ is defined as $(a,b) = ]a,b[ = \left \{ x \in \mathbb{R}|\,a&lt;x&lt;b\right \} $. It has two parameters $a$ and $b$. The sets of all open intervals, i.e. $\left \{  \left \{ x \in \mathbb{R}|\,a&lt;x&lt;b\right \} | a,b \in \mathbb{R}\right\}$ has a VC dimension of 2 for the reason you mention. Keep in mind that the VC dimension of a hypothesis set $H$ is the most points $H$ can shatter.). To put it graphically:



(image from CalTech's free machine Learning online course by Yaser Abu-Mostafa Learning from Data)