Category:Limits Superior
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This category contains results about Limits Superior.
Definitions specific to this category can be found in Definitions/Limits Superior.
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 maximum.
This maximum is called the limit superior.
It can be denoted:
- $\ds \map {\limsup_{n \mathop \to \infty} } {x_n} = \overline l$
Definition 2
The limit superior of $\sequence {x_n}$ is defined and denoted as:
- $\ds \map {\limsup_{n \mathop \to \infty} } {x_n} = \inf \set {\sup_{m \mathop \ge n} x_m: n \in \N}$
Subcategories
This category has only the following subcategory.
E
- Examples of Limits Superior (5 P)