What is Upper bound: Definition and 113 Discussions

In mathematics, particularly in order theory, an upper bound or majorant of a subset S of some preordered set (K, ≤) is an element of K which is greater than or equal to every element of S.Dually, a lower bound or minorant of S is defined to be an element of K which is less than or equal to every element of S.
A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound.
The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.

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  1. S

    Least Upper Bound: What Is It & How to Prove It

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  2. T

    Is there a relationship between upper and lower bounds in an ordered set?

    Let E be a nonempty subset of an ordered set; suppose \alpha is a lower bound of E and \beta is an upper bound of E . Prove that \alpha \leq \beta . So do I just use the following definition: Suppse S is an ordered set, and E \subset S . If there exists a \beta \in S such that...
  3. B

    Real Analysis related to Least Upper Bound

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  4. A

    Least Upper Bound Property

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  5. P

    Upper bound on exponential function

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  6. S

    Real Analysis- least upper bound and convergence

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  7. EnumaElish

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  8. N

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  9. P

    Proving c+1 is an Upper Bound of S with Completeness Axiom

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  10. P

    Upper Bound for Optimal Value in Max Problem

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  11. P

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  12. L

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  13. Oxymoron

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