Ball
High school
A ball is the set of all points within a distance $r$ of a center $c$. It is consists of the sphere together with everything inside it.
Undergraduate (metric spaces)
A ball is the set of all points within a distance $r$ of a center $c$: the sphere together with everything inside it. If the boundary of the ball is included in the set, then the ball is a closed ball:
\[\mathbb{B} = \setdef{x \suchthat d(x, c) \leq r}.\]If boundary is excluded, then it is called an open ball:
\[\mathbb{B} = \setdef{x \suchthat d(x, c) < r}.\]Examples
Examples
- A solid bowling ball High school
Non-examples
Things that may be mistaken for examples.
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The surface of a basketball
High school
The surface of a basketball is not a ball, because it does not include the inside.