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)