How is the topic "search for identidy" important in Oedipus Rex?

Getting a curse thrust upon you can be rough. Poor Oedipus gets one from birth stating that he would fulfill a pretty creepy prophecy of killing his father and marrying his mother. That's not exactly what every boy dreams of and is enough to mess with anyone's sense of identity. Oedipus does fulfill the prophesy but realizes he still doesn't know who he is and what he was meant to be.