Bounded from Below

A set is said to be bounded from below if it has a lower bound.

Consider the real numbers with their usual order. Then for any set M subset= R, the infimum infM exists (in R) if and only if M is bounded from below and nonempty.

See also

Bounded from Above, Greatest Lower Bound, Infimum, Lower Bound

This entry contributed by Roland Uhl

Explore with Wolfram|Alpha

Cite this as:

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

Subject classifications