Definition:Limit Inferior/Definition 2

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

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

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

Also see

Linguistic Note

The plural of limit inferior is limits inferior.

This is because limit is the noun and inferior is the adjective qualifying that noun.