Edwin, I generally agree that mathematics shouldn't be subordinated to physics.
But regarding your take on Relativity:
Observer A is moving 10 seconds (sec) in time and is considered to be at rest. Observer B is moving uniformly at .9c relative to A, and so moves 9 light-seconds (ls) in that time. According to Relativity, and the Lorentz transformation, they will each observe the other's clock to have only ticked 4.36 sec (t' = t(sqrt(1-.9^2)) = 10*sqrt(.19) = 4.36.
Now we need to consider the motion of a third body C relative to each. C is moving in the same direction as B. A and B will each agree that C passes a signpost at a definite point in space, but they will disagree on both how far away it is and at what time C reaches it.
The clock on C will be, like the signpost, objects agreed upon by A and B, and C's clock can be given by B as
t' = 4.36*sqrt(1-.9^2) = 1.9 sec.
So returning to A, given C's clock at a distance of 10 ls according to A, C's distance traveled in 10 sec on A's Clock will be given by
1.9 = 10(sqrt(1-s^2)) with s being the ls C travels in 10 sec on A's clock
.19 = sqrt(1-s^2)
.036 = 1-s^2
s^2 = 0.964
s = .98
So while A observes B to be moving at .9c and B observes C to be moving at .9c in the same direction, A observes C to be moving at .98c
You may think it absurd or counter-intuitive, but it is with Relativistic mathematics consistent with the physical world.
For a simple, graphic explanation of Special Relativity, see:
https://www.researchgate.net/publication/335989541_Special_Relativity_graphically_explained
