Upper Bound

analysis

Definition

Upper Bound

A sequence $(a_n{)}_{n{\ge }_0}$ is called bounded above if there exists a real number $S$ such that:

$$\exists S\in \mathbb{R}:\forall n\in \mathbb{N}:a_n\le S$$

Any such number $S$ is called an upper bound of that sequence.

The smallest upper bound is called the supremum of that sequence.