Thread: Two convergent subsequences, divergent sequence

I know that if a sequence has two subsequences that converge to different values than that sequence is divergent. However, I am asked to prove this fact. Any help is much appreciated.

The basic setup is to let two subsequences converge to two different values. Then to show the sequence doesn't converge, take a particular epsilon and show that you for all N sufficiently huge you can't be close to one limit value because you must be hitting the limits of the subsequences

Can you see a good epsilon to choose?