"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.

enter image description here


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