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[itex]|\frac{dx_i}{dt}|[/itex] is used when reference frame is at rest, so we define change in position of object w.r.t to that reference frame by it, but we are talking about a situation in which both the objects are moving and we use one of the objects as reference frame for other, so how will you define the change in position w.r.t to reference point in this case, certainly not by "[itex]|\frac{dx_i}{dt}|[/itex]", as both the objects are moving in which we use one as reference frame.The cosmic speed limit says that [itex]|\frac{dx_i}{dt}|<c[/itex] where [itex]x_i[/itex] is the position of some given massive object, i, in some given inertial reference frame. This doesnotimply that [itex]|\frac{d(x_i-x_j)}{dt}|<c[/itex]. Do you see that those are entirely different quantities?