mathematical physics - Finite or ∞ set of masses & ∃ gravity center?

Any finite & non empty set of masses has a computable center of gravity: $\vec{OG} = \frac{\sum_i m_i \vec{OM}_i}{\sum_i m_i}$ .

Does the contrapositive permits to conclude that a mass system with physical evidence that it doesn't have a gravity center is an infinite set of mass (i.e. of cardinal larger than $\aleph_0$) ?

On the other hand, an infinite set of masses may have a computable center of gravity. Ex. : within a 2D infinite plan, an infinite set of equal masses linearly distributed along the x and y axis will have a gravity center at its origin O. Unfortunately, this example doesn't have a center of gravity since the integral of masses in this particular topology doesn't converge.