= Radon's theorem
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= Intersecting convex hull partition theorem
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= Radon theorem
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Every <set> of at least $d+2$ points in $\mathbb R^d$ can be partitioned into two nonempty parts with intersecting <convex hulls>. To see this, take a nonzero <affine dependence> on $d+2$ of its points. Its positive and negative coefficient sums have the same magnitude $L>0$. Dividing by $L$ expresses one point as a <convex combination> of the positive-coefficient points and also as a <convex combination> of the negative-coefficient points. Distribute zero-coefficient and remaining points arbitrarily between the parts. This theorem obstructs arbitrary labels for <affine linear classifiers>.
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