Talk:Radon's theorem

Proof is formally incosistent
$$I$$ and $$J$$ are defined as sets of points of $$\mathbb{R}^d$$. However, in $$p= \sum_{i\in I}\frac{a_i}{A} x_i=\sum_{j\in J}\frac{-a_j}{A}x_j,$$ it says $$i\in I$$ and $$j \in J$$, indicating that $$I, J$$ contain a set of natural numbers. Shouldn't $$I$$ and $$J$$ be defined as a subset of $$\{1,2, \dots d+2\}$$ and accordingly the desired partition as $$\{x_i: i \in I\}$$ and $$\{x_i: i\in J\}$$. TheViking98868768763 (talk) 10:13, 3 May 2021 (UTC)
 * Easier fix is to replace $$i\in I$$ etc by $$x_i\in I$$. —David Eppstein (talk) 16:26, 3 May 2021 (UTC)
 * Now $$a_i$$ is not defined. $$A=\sum_{x_i\in I} a_i=-\sum_{x_j\in J} a_j.$$ doesn't make sense. TheViking98868768763 (talk) 19:52, 3 May 2021 (UTC)
 * It's defined at the start of the section, in the sentence " there exists a set of multipliers". One can reasonably expect readers to match the subscripts from the xi's to the ai's. —David Eppstein (talk) 21:32, 3 May 2021 (UTC)