Interval (mathematics)
Balls

An open finite interval (a, b) {\displaystyle (a,b)} is a 1-dimensional open ball with a center at 1 2 (a + b) {\displaystyle {\tfrac {1}{2}}(a+b)} and a radius of 1 2 (b − a). {\displaystyle {\tfrac {1}{2}}(b-a).} The closed finite interval {\displaystyle } is the corresponding closed ball, and the interval's two endpoints { a, b } {\displaystyle \{a,b\}} form a 0-dimensional sphere. Generalized to n {\displaystyle n} -dimensional Euclidean space, a ball is the set of points whose distance from the center is less than the radius. In the 2-dimensional case, a ball is called a disk.

If a half-space is taken as a kind of degenerate ball (without a well-defined center or radius), a half-space can be taken as analogous to a half-bounded interval, with its boundary plane as the (degenerate) sphere corresponding to the finite endpoint.
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