A point of a closed convex set?

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Homework Statement



Given D a a closed convex in R4 which consists of points [tex](1,x_2,x_3,x_4)[/tex] which satisfies that that [tex]0\leq x_2,0 \leq x_3 [/tex] and that [tex] x_2^2 - x_3 \leq 0[/tex]


The Attempt at a Solution



Then to show that either the point a: = (1,-1,0,1) or b:=(1,0,0,-1) is part of the convex set D.

They must satisfy the equation [tex]l = b \cdot t + (1-t) \cdot b [/tex] and

[tex]l = a \cdot t + (1-t) \cdot a [/tex] which proves that either of the two points lies on a line segment l which belongs to the convex set.

Am I on the right track?
 

Answers and Replies

  • #2
quasar987
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You want to show that a and b belong to D?

D has be entirely defined, and the fact that it is convex doesn't have anything to do with the problem as far as i can see. The second coordinate of a is negative, so it violates [tex]0\leq x_2[/tex].
 
  • #3
HallsofIvy
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And b is almost as trivial!
 

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