Dear Neville, The fact is that if you divide an inequality equation by -1 you change the sense of the inequality. 10 + -5 > 0 -10 + 5 < 0 When you divided your inequality you *assumed* that what you were dividing by was positive because you retained the '>'. For any given set of values for which the rest of you analysis is valid, whether this *assumption* is true or not depends entirely on which way round you label the particles. So whether (u1+v1) > (u2+v2) or (u1 + v1) < (u2 + v2) is also entirely *dependant* on your choice of labelling contrary to your conclusion that: "This [ (u1+v1) > (u2+v2) ] is a preposterous result, since even the decision to label them this way round in the first instance was totally arbitrary". That sentence was the entirity of your demonstration that momentum cannot be conserved in an inelastic collision. Regards, Mike.