Editing Interval (mathematics) (section)

=== Balls ===

An open finite interval <math>(a, b)</math> is a 1-dimensional open [[ball (mathematics)|ball]] with a [[center (geometry)|center]] at <math>\tfrac12(a + b)</math> and a [[radius]] of <math>\tfrac12(b - a).</math> The closed finite interval <math>[a, b]</math> is the corresponding closed ball, and the interval's two endpoints <math>\{a, b\}</math> form a 0-dimensional [[n-sphere|sphere]]. Generalized to <math>n</math>-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 (mathematics)|disk]].

If a [[half-space (geometry)|half-space]] is taken as a kind of [[degeneracy (mathematics)|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.