Let's say there are two sets of affine functions.
- $\mathcal{A} = \{ax +b \mid a,b \in \mathbb{R}\}$
- $\mathcal{H} = \{2x + 1, x, 3x + 4, 4x\}$
I know that the $\mathrm{Pdim}(\mathcal{A}) = 2$. From my understanding the $\mathrm{Pdim}(\mathcal{H})$ is also equal to 2 as I can find $\{x_1, x_2\}$ and $z_1, z_2$ such that for all subsets $T \subseteq \{x_1, x_2\}$, there is a function $f \in \mathcal{H}$ such that $\forall x \in T, f(x) \geq z_1$ and $\forall x \notin T f(x) < z_1$.
Is my intuition correct?