A set \(S\) is said to be convex if, for all \(x_1, x_2 \in S\) and all \(w \in [0,1]\), the point \(wx_1 + (1-w)x_2 \in S\).
A set \(S\) is said to be convex if, for all \(x_1, x_2 \in S\) and all \(w \in [0,1]\), the point \(wx_1 + (1-w)x_2 \in S\).