Given a hypothesis class H $,$ the VC dimension, $VC(H)$ is defined to be the size of the largest set that is shattered by H $.$ If H can shatter arbitrarily large sets, then we say that $VC(H)=.$

$4\mathrm{.}1$ It is sometimes useful to think of VC dimension as being related to the number of parameters needed to specify an element of $H.$ For example, what is the VC dimension of the set of hypotheses of the following form?

$h_o(x)=\{\begin{array}{ccc}1& if{}_d{x}^d+{}_{d-1}{x}^{d-1}+\text{c}\text{d}\text{o}\text{t}\text{s}& +{}_0>0\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

Please justify your answer.