A convex and a non-convex set
The intuitive idea of a convex set is best given by a picture.
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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).
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Non-convex sets may contain points such as |
A convex and a non-convex setThe intuitive idea of a convex set is best given by a picture.
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