In the second part of Republic, Book 1, Socrates agrees with Thrasymachus that in the precise sense of the word "ruler," a ruler never makes mistakes. But he points out that in the precise sense, a ruler also rules for the benefit of others not for his own benefit. The argument shifts to the question whether it is more profitable to be unjust than just, with Thrasymachus defending the former and Socrates arguing for the latter. Although Socrates appears to win the argument, Thrasymachus leaves the room and Socrates admits that he knows no more about the concept of justice than he did at the beginning of the discussion.