In mathematics, particularly in order theory, an **upper bound** or **majorant**[1] 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.[2][3]
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**[1] (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.[4]

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