this is for holding javascript data
Xavier Holt edited begin_lem_Two_point_sets__.tex
about 8 years ago
Commit id: 64fecf74d6262d716f93760abfb913cb79a61531
deletions | additions
diff --git a/begin_lem_Two_point_sets__.tex b/begin_lem_Two_point_sets__.tex
index 63c63ec..fc517d4 100644
--- a/begin_lem_Two_point_sets__.tex
+++ b/begin_lem_Two_point_sets__.tex
...
\end{lem}
\begin{proof}
($\Rightarrow$) by contradiction: Linear separability implies we can draw a line in the plane such that all $p\in \P$
are fall on one
side, side and all $q\in \Q$ the other. Can our convex hulls ever cross this line?
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 elements of $\P$ on either side of our separability line, a contradiction.