In the western culture, the definition of infinity and finiteness developed into various features, being combined with classical Hebraism and Hellenism, and after modernism, it has been paralleled with natural sciences within the circle of its tradition, whereas the definition of infinity has been showed in Buddhism, the traditional religion, which has been handed down without scientific consideration, in the eastern culture. This is the most notable characteristics between two hemispheres. In this paper, I will show sameness and differences of these two cultures in terms of defining infinity. Also in terms of examining the definition of infinity and finiteness in the Buddhist principles which has been handed down since 600∼500 B.C. I will show how the definition of Buddhist infinity connect with the mathematical definition of today.