在数学分析和有关的数学领域中，一个集合被称为有界的，如果它在某种意义上有有限大小。反过来说，不是有界的集合就叫做无界。

如果存在一个实数 k，使得对于所有 S 中的 s 有 k ≥ s，实数集合 S 被称为“上有界”的，这个数 k 被称为 S 的上界。可用类似的定义术语“下有界”和下界。

如果集合 S 有上界和下界二者，则它是有界的。所以，如果一个实数集合包含在有限区间内，则它是有界的。

"Bounded" and "boundary" are distinct concepts; for the latter see boundary (topology). A circle in isolation is a boundaryless bounded set, while the half plane is unbounded yet has a boundary.

In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size. Conversely, a set which is not bounded is called unbounded. The word bounded makes no sense in a general topological space without a metric.