Mathematics · Real Analysis

Let (a n ) n≥1 be a bounded sequence of real numbers such that lim n→∞ a n does not exist. Let S = {l &in; ℝ : there exists a subsequence of (a n ) converging to l}. Which of the following statements is necessarily true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

S has at least two elements

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Let (a n ) n&ge;1 be a bounded sequence of real numbers such that lim n&rarr;&infin; a n does not exist. Let S = {l &in; ℝ : there exists a subsequence of (a n ) converging to l}. Which of the following statements is necessarily true?