If the number K 1 exists so that f(x)≤K 1 holds for any x∈D, the function f(x) is said to have an upper bound on d.
On the other hand, if the number K2 exists, so that f(x)≥K2 is true for any x∈D, the function f(x) is said to have a lower bound on D, and K2 is called the lower bound on D. ..
If there is a positive number m, so that |f(x)|≤M holds for any x∈D, the function is said to be bounded on X. If there is no such m, the function f(x) is said to be unbounded on X.: Equivalent to, no matter for any positive number m, there is always x 1 belonging to x, so | f (x1) | >; M, the function f(x) is unbounded on x.
In addition, the necessary and sufficient condition for the function f(x) to be bounded on X is that it has both upper and lower bounds on X.
Extended data
Regarding the boundedness of functions, we should pay attention to the following two points:
The (1) function is bounded or unbounded in a certain interval, and both must belong to one;
(2) From the geometric point of view, it is easy to judge whether a function is bounded (see Figure 2). If two straight lines parallel to the X axis cannot be found to form the graph of the function between them, then the function must be unbounded, for example.
Baidu Encyclopedia-Boundedness of Functions
Baidu Encyclopedia-Boundedness