首先，看看仿射集和凸集的定義：
- A set C is affine if the line through any two distinct points in C lies in C.
- A set C is convex if the line segment between any two points in C lies in C.
倘若沒有注意到紅色部分，上面的定義看起來非常相似。但就是這麼一丁點文字上的不同，卻帶來了截然不同的東西。請看下面兩個命題：
- Any line is affine. If it passed through zero, it is a subspace, hence also a convex cone.
- A line segment is convex, but not affine (unless it reduces to a point).