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What I want to satisfy myself is that the "top velocity speed" between any two points is in fact a finite number despite the possibly infinite amount of resources that can be "thrown at " the experiment .

I think it may be been discovered even then?) that the Lorentz factor is verified by experiment but not "proved" as such.

So ,is there a mathematical procedure that ,in a finite system of small objects or particles would allow one to quantify relative motion between any two objects?