For obvious reasons, the self-diffusion coefficient in bounded many-body systems must be strictly zero, provided that it is defined as the limit of [R(t)–R(0)]2/(2td) whent grows indefinitely [d is the dimensionality,R() is the position of a given particle at time]. Thus, the time integral of the velocity correlation function is strictly zero. A system of hard points on a half-infinite line with a reflective wall at the origin does exhibit this property of absence of diffusion, since each particle has an average position. We study in detail the difference between the velocity correlation functions of the infinite and of the half-infinite systems.