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Upper and lower bounds

This article is about precise bounds. For asymptotic bounds, see Big O notation.
A set with upper bounds and its least upper bound

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]

  1. ^ a b Cite error: The named reference schaefer was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference MacLane-Birkhoff was invoked but never defined (see the help page).
  3. ^ "Upper Bound Definition (Illustrated Mathematics Dictionary)". Math is Fun. Retrieved 2019-12-03.
  4. ^ Weisstein, Eric W. "Upper Bound". mathworld.wolfram.com. Retrieved 2019-12-03.

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