Definition:Limit Inferior

Definition
Let $\sequence {x_n}$ be a bounded sequence in $\R$.

Also known as
The limit inferior is also called the lower limit, or just liminf.

However, note that the term lower limit has a subtly different meaning in the context of topology, so to avoid ambiguity its use here is not recommended.

Also see

 * Equivalence of Definitions of Limit Inferior


 * Definition:Lower Limit (Topological Space)
 * Relationship between Limit Inferior and Lower Limit


 * Definition:Limit Superior


 * Definition:Limit Inferior of Sequence of Sets for an extension of this concept into the field of measure theory.