Theorem 18.1 states that "Let f be a continuous real-valued function on a closed interval [a, b]. Then f is a bounded function.". Read the proof of Theorem 18.1 with [a, b] replaced by (a, b). Where does it break down? Explain.

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A: Both questions are different so I soved 1st queation if you want 2nd one then repost it again.

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A: This question is related to Real Analysis.