Explain the meaning of {an }

Question

Complete the following question:

By definition, lim_n→∞ a_n=L if for every ε>0, the re exists a positive number N such that if n is an integer with n>N, then |a_n-L|<ε. By taking the negation of this definition, write out the meaning of lim_n→∞ a_n ≠L using quantifiers.

Then write out the meaning of {a_n } diverges using quantifiers.