# A point of a closed convex set?

1. Jun 25, 2007

### Mathman23

1. The problem statement, all variables and given/known data

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

3. 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 $$l = b \cdot t + (1-t) \cdot b$$ and

$$l = a \cdot t + (1-t) \cdot a$$ 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?

2. Jun 26, 2007

### quasar987

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 $$0\leq x_2$$.

3. Jun 26, 2007

### HallsofIvy

Staff Emeritus
And b is almost as trivial!