This is Problem x12.26 from Moschovakis: Notes on Set Theory.
In order to save time of helpers, I want to mention that the same problem was posted in several forums:
Art of Problem Solving • View topic - Cantor canonical form
S.O.S. Mathematics CyberBoard :: View topic - Cantor canonical form (I tried to give a solution here.)
Cantor canonical form
(In my opinion, the OP should have done this, or at least he/she should post a message like this after he gets a satisfactory answer in one of the forums.)