The following question has been puzzling me for a few days:

Assume (a_{n})^{∞ }_{n=1}is a convergent sequence of integers. Prove the existence of N ∈Nsuch that a_{i}= a_{j}for all i, j > N.

I am failing to interpret the meaning of the a_{i }= a_{j}. I understand that I need to prove the existence of a cutoff point, meaning I will probably need to fix an epsilon, etc. Using triangle inequalities may also be useful, I'm not sure, maybe none of those ideas are right.

I am still fairly new to calculus so any help understanding this problem and would be appreciated.

K.