An interval is considered bounded if both endpoints are real numbers. An interval is unbounded if both endpoints are not real numbers. Replacing an endpoint with positive or negative infinity—e.g., (−∞,b] —indicates that a set is unbounded in one direction, or half-bounded.

Is the empty set a bounded interval?

The empty set is bounded, and the set of all reals is the only interval that is unbounded at both ends. Bounded intervals are also commonly known as finite intervals.

What does it mean if a function is bounded?

In mathematics, a function f defined on some set X with real or complex values is called bounded if the set of its values is bounded. In other words, there exists a real number M such that. for all x in X. A function that is not bounded is said to be unbounded.