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.

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.

*This entry contributed by Roland Uhl*

Uhl, Roland. "Bounded from Above." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/BoundedfromAbove.html