# Example of Proof of Radon's theorem

"By mathematical induction. Let proposition $$P_n$$ be Helly’s Theorem in the case of n subsets in $$\mathbb{R}^d$$. Since $$n > d$$, we can use $$P_{d+1}$$ as our base case. $$P_{d+1}$$ is clearly true, because if the intersection of $$d + 1$$ of them are non-empty, then the intersection of all of them are non-empty."

I found the above statement from here and constructed the following example(pic)

If $$d=0$$ then there is only one subset since they are all convex if $$d+1$$ of those meet at one point then all would meet at one point.

I want to know if my example and explanation is correct and want to know about more examples.