# Category:Examples of Limits Inferior

This category contains examples of Limit Inferior.

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

### Definition 1

Let $L$ be the set of all real numbers which are the limit of some subsequence of $\sequence {x_n}$.

From Existence of Maximum and Minimum of Bounded Sequence, $L$ has a minimum.

This minimum is called the limit inferior.

It can be denoted:

$\displaystyle \map {\liminf_{n \mathop \to \infty} } {x_n} = \underline l$

### Definition 2

The limit inferior of $\sequence {x_n}$ is defined and denoted as:

$\displaystyle \map {\liminf_{n \mathop \to \infty} } {x_n} = \sup \set {\inf_{m \mathop \ge n} x_m: n \in \N}$

## Pages in category "Examples of Limits Inferior"

The following 5 pages are in this category, out of 5 total.