I've been thinking in circles over this problem so I thought I'd give this forum a try - I hope someone can help.
I've been given a definition:
For all epsilon>0 , there exists a natural number N such that if |Xn-L| < epsilon, then n is greater than or equal to N.
I need to either find an infinite sequence Xn which converges but does not satisfy the conditon above OR
find a sequence Xn and L which do satisfy the condition above but Xn does not converge to L.
I'd be grateful if anybody could talk me through what features such a sequence should have.