\begin{definition}[Definition:Infimum of Set/Real Numbers]
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 $\R$.
If there exists an '''infimum''' of $T$ (in $\R$), we say that '''$T$ admits an infimum (in $\R$)'''.
The '''infimum''' of $T$ is denoted $\inf T$ or $\map \inf T$.
\end{definition}