I am trying to find VC-dim $d$ of all linear threshold functions in $\mathbb{R}^n$.
I know how to show, using Radon's theorem, that $d < n+2$, and i know that i should show somehow, that simplex in $\mathbb{R}^n$ is an example of a set which gives the result $VC(\mathbb{R}^n,\: \mathcal{H}) = n+1$. However, i don't know how to show that we are able to get every subset of simplex vertecies intersecting it with half spaces. Can you help me?