Definition
Limit Superior
The limit superior (or upper limit) of a sequence
is the largest limit point of the sequence, including improper limit points. It is denoted by: Every sequence of real numbers has a limit superior in the extended real number system
.
Properties
- Relation to Limit: A sequence converges to
if and only if . - Boundedness: For any
, for almost all , and for infinitely many . - Inequality: It always holds that
.