Parameters measuring the size of set families - Combinatorial Parameters

The VC dimension of a family $\mathcal{H}$, denoted by $\VC(\mathcal{H})$, is the largest integer $d$ such that there exists a set $S\subset \mathcal{X}$, of size $d$ such that $S$ is shattered by $\mathcal{H}$, i.e. $$ |\mathcal{H|_{|S}} = 2^{|S|}\,. $$

Vapnik-Chervonenkis Dimension [vc71].