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Xavier Holt edited begin_lem_Two_point_sets__.tex
about 8 years ago
Commit id: e7804e99334bd2866a84b0e2fec9a76353d73ae9
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WLOG let's assume that $C(\P)$ crosses this line. This means one of the line-segments of $C(\P)$'s boundary crosses our line. All such line-segments are defined between two points of $C(\P)$. As such we have an element of $\P$ on either side of our separability line, a contradiction.
($\Leftarrow$) follows immediately from the fact that $\P,\Q$ are subsets of their respective convex-hulls. If all of $C(\P)$ is on the side of a line, $\P \subset C(\P)$ is on the same side.
\end{proof}
\end{proof} \begin{lem}
Two convex hulls are linearly separable implies they do not intersect.
\end{lem}