Myself and himself you might call them, or the on the other hand the one alter ego of the other. Certainly this meeting has been seen as too much for No.6 to bear, in finding out that he is in fact No.1, and has been so all along. How he then goes berserk, chasing No.1 round the control room, then launching the rocket in order to destroy his alter ego and the village into the bargain.
Of course this is not the first time that No.6 has met up with himself. There was that time with the schizoid man, Curtis. Of course that might have been Curtis, although he might have been No.1!