- #1

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*(x*be a bounded sequence that diverges. Show that there is a pair of convergent subsequences

_{n})*(x*and

_{nk})*(x*, so that

_{mk})[tex]

lim_{k\rightarrow\infty}

[/tex] [tex]\left|x_{nk} - x_{mk}\right| > 0[/tex]

lim_{k\rightarrow\infty}

[/tex] [tex]\left|x_{nk} - x_{mk}\right| > 0[/tex]