What does it mean if you take the zero vector in the hyperplane separation theorem?












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$begingroup$


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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$endgroup$








  • 1




    $begingroup$
    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 $uvnotlt uw$.
    $endgroup$
    – John Douma
    Jan 15 at 21:03
















0












$begingroup$


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?










share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    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 $uvnotlt uw$.
    $endgroup$
    – John Douma
    Jan 15 at 21:03














0












0








0





$begingroup$


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?










share|cite|improve this question









$endgroup$




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?







separation-axioms






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 15 at 20:32









Ronny LeleuRonny Leleu

11




11








  • 1




    $begingroup$
    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 $uvnotlt uw$.
    $endgroup$
    – John Douma
    Jan 15 at 21:03














  • 1




    $begingroup$
    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 $uvnotlt uw$.
    $endgroup$
    – John Douma
    Jan 15 at 21:03








1




1




$begingroup$
The theorem states that there exists a $u$; you cannot choose it.
$endgroup$
– angryavian
Jan 15 at 20:35




$begingroup$
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






$begingroup$
The separation theorem gives the existence of a non zero $u$.
$endgroup$
– copper.hat
Jan 15 at 20:37














$begingroup$
If $u=0$ then $uvnotlt uw$.
$endgroup$
– John Douma
Jan 15 at 21:03




$begingroup$
If $u=0$ then $uvnotlt uw$.
$endgroup$
– John Douma
Jan 15 at 21:03










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