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A set of numbers is said to be bounded above, if we can find a number which is larger than any number in the set. Such a number is called an upper bound for the set. Similarly, a set is bounded below by a number, called a lower bound, which is smaller than any number in the set. If a set is bounded both above and below, we just say that it is bounded.
Often the word bounded is used for functions, when it means that the range of the function is a bounded set.