A set is said to be bounded from above if it has an upper bound.
Consider the real numbers with their usual order. Then for any set 
, the supremum 
exists (in 
) if and only if 
is bounded from above and nonempty.
Bounded from Above
See also
Bounded from Below, Least Upper Bound, Supremum, Upper BoundThis entry contributed by Roland Uhl
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Uhl, Roland. "Bounded from Above." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/BoundedfromAbove.html