Bounded from Above

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 M subset= R, the supremum supM exists (in R) if and only if M is bounded from above and nonempty.

See also

Bounded from Below, Least Upper Bound, Supremum, Upper Bound

This entry contributed by Roland Uhl

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Cite this as:

Uhl, Roland. "Bounded from Above." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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