Hi, my question is:
Let L be a real number and let (a_n) be a sequence of real numbers that does not converge to L (that is, it is either divergent or its limit is not equal to L). Use the definition of convergence to L to show that for some e greater than 0, (a_n) has a subsequence (a_n(_k)) such that (a_n(_k)) isn't in the interval (L - e, L+e) for all natural numbers k.
Any help would be hugely appreciated