In mathematics, a ball is the inside of a sphere; both concepts apply not only in the three-dimensional space but also for lower and higher dimensions, and for metric spaces in general.
In higher mathematics, a careful distinction is made between the surface of a sphere (referred to as a “sphere”), and the inside of a sphere (referred to as a “ball”). Thus, a sphere in three dimensions is considered to be a two-dimensional spherical surface embedded in three-dimensional Euclidean space, while a ball is a solid figure bounded by a sphere.
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