Using the given that the sequence {1/n} converges to 0, prove that none of the following assertions are equivalent to the definition of convergence of a sequence {an} to the number a:

a. For some ε>0 there is an index N such that

|an-a|<ε for all indices n≥N.

b. For each ε>0 and each index N

|an-a|<ε for all indices n≥N.

c. There is an index N such that for every number ε > 0,

|an-a|<ε for all indices n≥N.