(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a problem from D'Inverno's "Introducing Einstein's Relativity".

If v_{AB}is the velocity of B with respect to A, v_{BC}is the velocity of C with respect to B, and v_{AC}is the velocity of C with respect to A (all velocities are in relativistic units, that is, c=1), prove that if 0<v_{AB}<1 and 0<v_{BC}<1, then v_{AC}<1.

2. Relevant equations

The problem should be resolvable with just the equation

v_{AC}=(v_{AB}+v_{BC})/(1+v_{AB}v_{BC}).

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.

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# Homework Help: Proof regarding composition of velocities

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