Show that a bounded sequence in R that does not converge has more than one subsequential limit. That is, show that a nonconvergent bounded sequence has two subsequences each with a different limit.
Show that a bounded sequence in R that does not converge has more than one subsequential limit. That is, show that a nonconvergent bounded sequence has two subsequences each with a different limit.
I'd try by absurd : Suppose that every subsequences of the bounded sequence converge to the same limit. If you can show that the sequence converges then you're done.