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Of course, using the most abstract definition is not the best idea, but anything equivalent to the standard terminology is ok. For example, in 2d, we can san sa
by chaoxu 12y ago
Of course, using the most abstract definition is not the best idea, but anything equivalent to the standard terminology is ok. For example, in 2d, we can san say the convex hull of a finite set of points is the smallest enclosing convex polygon.
The name convex hull is related to linear hull and conic hull, therefore defining it to not contain the interior is strange, but reasonable because in many applications we only care about the description of the convex hull by describing the polygon.
- Tloewald 12y agoWell in abstract there are plenty of possible spaces where a set can be bounded but its boundary does not exist within the set (e.g. consider the transcendentals between 0 and 1) so talking about the "hull" as a boundary is completely useless. Even so, picking the word "hull" was perhaps careless. A lot of people, even mathematicians, are confused on the definition of circle vs. sphere (the circle is the boundary, the sphere is the volume), so even if you use these terms "correctly" you probably want to define your understanding of them.