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If you have two disjoint sets V and W, which are compact and convex, then by the separation theorem there exists a vector u such that uv< uw.

However what does it mean if you take u=0?

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    $\begingroup$ The theorem states that there exists a $u$; you cannot choose it. $\endgroup$ – angryavian Jan 15 at 20:35
  • $\begingroup$ The separation theorem gives the existence of a non zero $u$. $\endgroup$ – copper.hat Jan 15 at 20:37
  • $\begingroup$ If $u=0$ then $uv\not\lt uw$. $\endgroup$ – John Douma Jan 15 at 21:03

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