Interactive Real Analysis - part of MathCS.org

Next | Previous | Glossary | Map | Discussion

Let A be an ordered set and X a subset of A. An element b is called a lower bound for the set X if every element in X is greater than or equal to b. If such a lower bound exists, the set X is called bounded below.

Let A be an ordered set, and X a subset of A. An element b in A is called a greatest lower bound (or infimum) for X if b is a lower bound for X and there is no other lower bound b' for X that is greater than b. We write b = inf(X).

By its definition, if a greatest lower bound exists, it is unique.

Next | Previous | Glossary | Map | Discussion