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+\subsection*{Exercise 05}
+\begin{flushleft}
+$\text{(1) } \exists\ \alpha \in R \ni  x \geq  \alpha \ \forall  x \in  A$ \\
+$\text{(2) } \exists\ \alpha \in R \ni -x \leq -\alpha \ \forall -x \in -A$ \\
+\end{flushleft}
+
+\begin{flushleft}
+(1) $\implies  \alpha = \inf( A)$ \\
+(2) $\implies -\alpha = \sup(-A)$
+\end{flushleft}
+
+\begin{flushleft}
+Obviously, $a = -(-a) \implies \inf(A) = -\sup(-A)$
+\end{flushleft}