# Thread: Sequence Question for Real Analysis

1. ## Sequence Question for Real Analysis

Let (x_n) be a sequence of real numbers. Show that either there is some subse-quence (x_nk ) with x_nk --> infinity or with x_nk-->-infinity or there is some subsequence which converges

2. Originally Posted by flaming
Let (x_n) be a sequence of real numbers. Show that either there is some subse-quence (x_nk ) with x_nk --> infinity or with x_nk-->-infinity or there is some subsequence which converges
Hint: Every sequence has a monotone subsequence.