Let(adsbygoogle = window.adsbygoogle || []).push({}); (xbe a bounded sequence that diverges. Show that there is a pair of convergent subsequences_{n})(xand_{nk})(x, so that_{mk})

[tex]

lim_{k\rightarrow\infty}

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

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# Pair of convergent subsequences

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