A function f is bounded if there is a number h such that for all x from the domain D (f) one has-h f (x) h, that is, | f (x)| h.
Bounded Sequence. A sequence is bounded if it is bounded above and below, that is to say, if there is a number, k, less than or equal to all the terms of sequence and another number, K' , greater than or equal to all the terms of the sequence. Therefore, all the terms in the sequence are between k and K '. k ≤ an ≤ K'. How do you say There are bound to be.... as in There are bound to be a lot of people at the party, There are bound to be some exceptions to the rule.. | 1  2495 views. Answers. Best Answer: bounded is referring to the fact that it is finite. and it makes sense since on an infinite set you might not ever find an absolute max/min since some where some how you might find a larger/smaller value. Source(s): James Stewarts multivariable Calculus book (5e) 15.7. Furthermore, we will say that is bounded below, if and only if, there exists a number m such that. , for any. The number m is called a lower-bound. Example: The sequence is bounded below by 0 (because it is positive). It is not bounded above. Example: The sequence is bounded. Indeed, we have for any, . We say that a real function f is bounded from above if there is a number K such that for all x from the domain D (f) one has f (x) K. We say that a real function f is bounded if it is bounded both from above and below. Equivalently, a function f is bounded if there is a number h such that for all x from the domain D (f) one has-h f (x) h, that is, | f (x)| h.
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how do you say bounded