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Concept# Upper and lower bounds

Summary

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 that 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 that 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.
Examples
For example, 5 is a lower bound for the set S = (as a subset of the integers or of the real numbers, etc.), and so is 4. On the other hand, 6 is not a lower bound for S since it is not smaller than every

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