Definition:Limit Superior/Definition 2

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

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

$\displaystyle \map {\limsup_{n \mathop \to \infty} } {x_n} = \inf \set {\sup_{m \mathop \ge n} x_m: n \in \N}$

Also see

Linguistic Note

The plural of limit superior is limits superior.

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