# Thread: How to prove that X={(x1, x2) | x2-3 >= -x1^2, x1, x2 >= 0} is a convex set?

2. ## Re: How to prove that X={(x1, x2) | x2-3 >= -x1^2, x1, x2 >= 0} is a convex set?

A set $C$ in $S$ is said to be convex if, for all $x$ and $y$ in $C$ and all $t$ in the interval $[0,1]$, the point $(1-t ) x + t y$ is in $C$. Convex set - Wikipedia, the free encyclopedia

Are you sure it is $X=\{(x_1, x_2) | x_2 - 3 \ge -x_1^2, x_1, x_2 \ge 0\}$ and not $X=\{(x_1, x_2) | x_2 - 3 \le -x_1^2, x_1, x_2 \ge 0\}$