Definition: Let and be two real numbers , and , a number set

is called neighborhood of point , denoted as

.

Among them, point is called the center of the neighborhood, is called the radius of the neighborhood. interval

and

They are respectively called the left neighborhood and right neighborhood of of point  . as the picture shows.

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        The left neighborhood of point is denoted as：

;

        The right neighborhood of point is denoted as：

.

        If the center of the neighborhood  is removed, the resulting neighborhood is called the centroided  neighborhood of point  , denoted as  , that is

　　More generally, any open interval centered on is the neighborhood of point . When the radius of the neighborhood does not need to be specifically identified, it can be abbreviated as .