In
mathematics, especially in
order theory, an
upper bound of a
subset S of some
partially ordered set (
K, =) is an element of
K which is
greater than or equal to every element of
S. The term
lower bound is defined
dually as an element of
K which is less than or equal to every element of
S. A set with an upper bound is said to be
bounded from above by that bound, a set with a lower bound is said to be
bounded from below by that bound. The terms
bounded above (
bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.