Tom,
Instead of providing a counterexample, you confirmed what I wrote: "an observer on the ground cannot be at the same instant in the train" and you added "That's why both frames are valid, without preference". Of course, frame A is valid for A and frame B is at the same instant valid for B. Well, "All the laws of motion apply in every observer's frame." The question is, how can the perspective of an observer at A be also the perspective of an observer at B if A and B are moving relative to each other? The Doppler effect describes why and how a person on the ground perceives the length of a train shorter than it really is as long as it is approaching but enlarged after subsequent departure.
So called Relativity attributes a length contraction to the moving part in both cases, decreasing as well as increasing distance because the Relativistic length contraction depends on the squared velocity which results mathematically simply from c/(c-v) + c/(c+v) = 2c^2/(c^2-v^2).
Einstein distinguished between the moving system and the system at rest instead to symmetrically only consider the relative motion.
In all, Relativity is logically the opposite of relativity and symmetry.
I reiterate: "So far you proved also unable to give an example for a concrete item in the real world that has measure zero or measure actual infinity."
You blamed me for not understanding: "I have. I won't take responsibility for your understanding." Did you really not understand the meaning of "a concrete item in the real world"?
Eckard
