Let $X\subset \mathbb{R}$ be a subset of the real line. Then the following two statements are logically equivalent:\begin{enumerate}\item $X$ is bounded and connected.\newline\item $X$ is a bounded interval.\end{enumerate}

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Analysis I

Exercise 11.1.1 (Bounded and connected subsets of real line are intervals)

Let $X \subset ℝ$ be a subset of the real line. Then the following two statements are logically equivalent: