Closed and Bounded Sets

Closed and bounded sets are concepts in mathematics that describe specific properties of collections of points in space. A set is **closed** if it contains all its limit points—meaning, if you have a sequence of points getting closer to some point within the set, that point is also in the set. A set is **bounded** if all its points lie within some fixed distance from a central point, so it doesn't stretch out infinitely. Together, these properties help define well-behaved sets, especially in calculus and geometry, and are key to many theorems in mathematics.