Infimum

analysis

Definition

Infimum

The greatest lower bound $I$ of a sequence is called the infimum. Thus, the infimum $\inf a_n$ is a real number $I_0$, such that the following properties are fulfilled:

1. $\forall n\in \mathbb{N}:a_n\ge I_0$
2. $\forall n\in \mathbb{N}:a\ge I⟹I_0\ge I$

If the sequence is not bounded below, $\inf a_n=-\infty$.