# machine learning – Pseudo-dimesnon of a subset of affine functions

Let’s say there are two sets of affine functions.

1. $$mathcal{A} = {ax +b | a,b in mathbb{R}}$$
2. $$mathcal{H} = {2x + 1, x, 3x + 4, 4x}$$

I know that the $$Pdim(mathcal{A}) = 2$$. From my understanding the $$Pdim(mathcal{H})$$ 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?