How is a limit of a convergence sequence of complex numbers unique?

This question in my text doesn't even seem like english to me, can anyone please help me get going on it.





Q. Show that a limit of a convergent sequence of complex numbers is unique by appealing to the corresponding result for a sequence of real numbers?





What does all that mean?|||A couple things.





1. Convergence of a sequence of complex numbers is equivalent to the convergence of the real and imaginary parts separately. So you can just use the corresponding result for convergence of a real sequence here.





2. Uniqueness is shown by assuming that lim z[n] = a and lim z[n] = b, then showing that a = b. So, no matter how you find the limit of the sequence, you have to always get the same answer. Use the standard definition of convergence:





(z[n]) converges to a if, for all eps%26gt;0 there is some N, such that whenever n%26gt;N, |z[n] - a| %26lt; eps.|||Prove it by contradiction.





1) Assume two limits, z1 and z2.


2) Let e = |z1-z2| / 2.


3) If the sequence converges to z1, then show it's impossible to find n(e) such that |z_n - z2| %26lt; e for n%26gt;n(e).|||i think u can solve that by induction