I reinforce my education through self-study of Machine Learning. When I come across the problem of Growth Function generated by Convex Set I see only the result and skimming over a proof. I have to accept that $m_{H}(N)=2^{N}$, where $H$ consists of all hypothesis in two dimensions $h:\mathbb{R}^{2}\rightarrow\{-1,1\}$. In every material I've studied authors skim over the proof. Even wiki on the subject of "Shattered set" skim over the problem, and one can read: "With a bit of thought, we could generalize that any set of finite points on a unit circle could be shattered by the class of all convex sets".
Could anyone explain it in simple words and show the proof why for the two-dimensional space when we put all $N$ points on the unit circle then the growth function equals to $2^N$?