# Upper and Lower Limits of a Bounded Sequence

The greatest and smallest limit points of a bounded sequence, as given by the preceding tutorial, are respectively called the **upper** (or superior) and **lower** (or inferior) **limits** of the sequence.

The upper limit of a bounded sequence is denoted by or . Similarly, the lower limit is denoted by or . Evidently, .

For bounded , the limits shall also be defined as

where are defined by , .