Prove that centre of mass is a unique point
I started with O as origin.G as CM and G' as assumed 2nd CM in the same sysyem of particles.
OG=R=(1/M) sum(i) [m_i*r_i]
OG'=R'=(1/M) sum(k) [m_k*r'_k]
The problem is theere is no unique relation between r_i and r'_k