- #1

bolzano07

- 1

- 0

*(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]