If a real sequence $X$ is divergent, then does a divergent subsequence $X'\neq X$ exist. I know how to prove this for a specific limit. That is if X does not converge to L then there exist a subsequence X' not equal to X such that X' does not converge to L. How do i extrapolate from here?
2026-03-27 06:09:51.1774591791
Divergent subsequence of a divergent sequence
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