Current physics has not yet provided a complete mathematic and quantitative description for a life system. In our previous work, we proposed to introduce the concept of positive information into physics. We defined positive information as the connection a system has with others and the order within itself. We defined the negative information as the disorder and disconnection within a system, which corresponds to the entropy in current physics theory. We showed how to calculate positive information. In this paper, we study how to use the concept of positive information to mathematically define the life system and explain the purpose of life.