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- Definitions: A set is bounded above by the number A if the number A is higher than or equal to all elements of the set. A set is bounded below by the number B if the number B is lower than or equal to all elements of the set.
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Apr 25, 2017 · A set is bounded above by the number #A# if the number #A# is higher than or equal to all elements of the set. A set is bounded below by the number #B# if the number #B# is lower than or equal to all elements of the set.
Key Questions. What is boundedness? Answer: Boundedness is about having finite limits. In the context of values of functions, we say that a function has an upper bound if the value does not exceed a certain upper limit. More... Explanation: Other terms used are "bounded above" or "bounded below".
A is bounded above (or right bounded) iff there is q ∈ F such that. (∀x ∈ A) x ≤ q. In this case, p and q are called, respectively, a lower (or left) bound and an upper (or right) bound, of A. If both exist, we simply say that A is bounded (by p and q).
Feb 10, 2013 · Bounded means bounded above and below. The function −x2 − x 2 is not bounded. In most applications to algorithms, it doesn't matter, since the functions are naturally non-negative, so are bounded below by 0 0. But in principle one should be careful.
5 days ago · A set is said to be bounded from above if it has an upper bound. Consider the real numbers with their usual order. Then for any set M subset= R, the supremum supM exists (in R) if and only if M is bounded from above and nonempty.
A sequence is said to be bounded above if there exists a real number M such that every term in the sequence is less than or equal to M. The smallest such M is called the least upper bound or supremum.
Being bounded from above means that there is a horizontal line such that the graph of the function lies below this line. Bounded from below means that the graph lies above some horizontal line. Being bounded means that one can enclose the whole graph between two horizontal lines.
