The sequence { 1/n } converges to 0 and that it does not converge to any other number. Using this fact prove that NONE of the following assertions is equivalent to the definition of convergence of a sequence {an} to the number a.

a. for some e>0, there is an index N such that |an -a| < e for all indices n>=N

b. for each e>0 and each index N, |an - a| < e for all indices n>=n

Can anyone give me a hint or an outline about this. i am totally clueless about it.