Hi there
How would I go about proving that "S= (x1,x2): x1 + x2 ≤ 1 , x1 ≥ 0)" is a convex set?
Thanks
*Sorry for the title typo
Take any two points $\displaystyle u:=(x_1,x_2),\,v:=(y_1,y_2)\in S$ ; you must prove that $\displaystyle tu+(1-t)v\in S\,,\,\,\forall\,t\in [0,1]$:
$\displaystyle tu+(1-t)v=\left(tx_1+(1-t)y_1,\,tx_2+(1-t)y_2\right)$ , and now you have the simple task yo show that:
1) $\displaystyle tx_1+(1-t)y_1\geq 0$ ;
2) $\displaystyle tx_1+(1-t)y_1+tx_2++(1-t)y_2\geq 1$ ...
Tonio