Definition:Infimum of Set/Real Numbers

Definition
Let $T \subseteq \R$.

A real number $c \in \R$ is the infimum of $T$ in $\R$ iff:


 * $(1): \quad c$ is a lower bound of $T$ in $\R$
 * $(2): \quad d \le c$ for all lower bounds $d$ of $T$ in $\R$.

The infimum of $T$ is denoted $\inf T$.

If there exists an infimum of $T$ (in $\R$), we say that $T$ admits an infimum (in $\R$).

Also see

 * Definition:Supremum of Subset of Real Numbers


 * Supremum and Infimum are Unique