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+\subsection*{Exercise 04 (Gapry)}
+Let $S$ is an ordered set, and let $E$ be a non-empty subset of $S$, so there exists $x \in E$.
+
+$\alpha$ is a lower bound of $E$, so $\alpha \le x$,
+
+$\beta$ is an upper bound of $E$, so $x \le \beta$,
+
+Combined, we have $\alpha \le x \le \beta$, so $\alpha \le \beta$
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