“…In this paper, we shall investigate the arithmetic on the middle-third Cantor set. Arithmetic on the fractal sets has some connections to the geometric measure theory, dynamical systems, and number theory, see [2,3,4,5,6,7,8,9,12,15,16,18,19,20] and references therein. However, relatively few papers investigate the structure of the fractal sets under some arithmetic operations.…”