Similarly, if there is a real number m that makes f (x) >: =m hold for all x∈D, then F is said to have a lower bound, and M is a lower bound of F. ..

If f has both upper and lower bounds, it is called bounded, otherwise it is called unbounded.

2.[ 1, 3] is a closed interval, which contains the boundary of two numbers, that is, all real numbers of 1-3. These two numbers 1, 3 are boundaries, and if they are (1, 3), they are open intervals, excluding 1, 3 of the boundaries.

Examples of extended data: Let E be a point set on the plane, P be a point on the plane, if P has neighborhood points, P is called an interior point of E ... If all points of the point set E are interior points, then E is called an open set.

Connected open sets are called regions or open sets. For example:

An open area together with its boundary is called a closed area. For example:

For point set E, if there is a positive number k, so that the distance between all points and point A does not exceed k, that is, everything holds, then E is called bounded point set, otherwise it is called unbounded point set.

For example, it is a bounded closed area. This is an unbounded open area.