Lower Bound

analysis

Definition

Lower Bound

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

$$\exists I\in \mathbb{R}:\forall n\in \mathbb{N}:a_n\ge I$$

Any such number $I$ called an lower bound of that sequence. If the sequence is not bounded below, $\inf a_n=-\infty$.

The greatest upper bound is called infimum the of that sequence.