Find evidence of Oedipus' greatness both in position and character in The Oedipus Plays.
Well, the fact that Oedipus became King of Thebes obviously indicates the kind of position that he attained in his life thanks to the way he conquered the sphinx and saved Thebes. However, the plays as a whole seem to point towards a curious contradiction in his character. That he was great is not at all questioned, however, his downfall seems to be linked precisely to his greatness. Consider what the Chorus says about the character of Oedipus at the end of Oedipus the King:
People of Thebes, my countrymen, look on Oedipus. He solved the famous riddle with his brilliance, he rose to power, a man beyond all power. Who could behold his greatness without envy? Now what a black sea of terror has overwhelmed him. Now as we keep our watch and wait the final day, count no man happy till he dies, free of pain at last.
Oedipus is therefore clearly presented as a person characterised by his "brilliance," but it also seems to suggest that the downfall of Oedipus was explicitly linked to his rise to power and greatness.In a sense, the Chorus suggests, Oedipus fell precisely because he overreached himself by being a man "beyond all power." Therefore, whilst the greatness of Oedipus is clearly indicated, both in his character and in his position, the Chorus uses him as an example to warn against reaching to high and placing ourselves in a position where we have too much power.