Interactive Real Analysis - part of MathCS.org

Next | Previous | Glossary | Map | Discussion

Definition 3.4.1: Lim Sup and Lim Inf

Let be a sequence of real numbers. Define
Aj = inf{ aj , aj + 1 , aj + 2 , ...}
and let c = lim (Aj). Then c is called the limit inferior of the sequence .

Let be a sequence of real numbers. Define

Bj = sup{ aj , aj + 1 , aj + 2 , ...}
and let c = lim (Bj). Then c is called the limit superior of the sequence .

In short, we have:

  1. lim inf(aj) = lim(Aj), where Aj = inf{aj , aj + 1 , aj + 2 , ...}
  2. lim sup(aj) = lim(Bj), where Bj = sup{ aj , aj + 1 , aj + 2 , ...}
Next | Previous | Glossary | Map | Discussion