| # A convex and a non-convex set The intuitive idea of a convex set is best given by a picture.
| A convex set in . For any two pair of points, such as and , the line segment joining the two points is entirely in the set. Note that if the two points are chosen to be those indicated in red, the line segment is at the boundary in this case — but that is OK, provided the set is closed (it contains its boundary).
| Non-convex sets may contain points such as and , with the line segment that joins them not entirely included in the set.