1. The problem statement, all variables and given/known data This is a problem from D'Inverno's "Introducing Einstein's Relativity". If vAB is the velocity of B with respect to A, vBC is the velocity of C with respect to B, and vAC is the velocity of C with respect to A (all velocities are in relativistic units, that is, c=1), prove that if 0<vAB<1 and 0<vBC<1, then vAC<1. 2. Relevant equations The problem should be resolvable with just the equation vAC=(vAB+vBC)/(1+vABvBC). 3. The attempt at a solution I understand that there are other ways to prove this, but I want to know this particular approach. I suspect it boils down to showing that the numerator is less than the denominator. I have tried reducing the denominator and/or increasing the numerator to find a greater expression that is less than one, but so far nothing has worked. I know this is really just a mathematical proof and has little to do with conceptual relativity, but I'd still like the solution.