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Upper and lower bounds
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, particularly in <a href="/facts/Order_theory/gn6fM3oJ">order theory</a>, an upper bound or majorant of a <a href="/facts/Subset/SJGERmbA">subset</a> S of some <a href="/facts/Preorder/uubzHSWm">preordered set</a> (<i>K</i>, ≤) is an <a href="/facts/Element_(mathematics)/Q2mx1vHL">element</a> of K that is <a href="/facts/Greater_than_or_equal_to/qkze4zdI">greater than or equal to</a> every element of S. <a href="/facts/Duality_(order_theory)/TTTcqYQy">Dually</a>, 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. </p>